The Quadratic Formula · MCQ assessment
Version A
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right123456789101112131415
/ 15
1Choose the two roots of $(2x - 3)(5x - 4) = 0$.
Ax = 3/2 or x = 4/5Bx = -3 or x = -4Cx = 3/2 or x = -4/5Dx = -3/2 or x = -4/5
2Work out the value of the discriminant $b^2 - 4ac$ for $3x^2 + 7x - 5 = 0$.
A67B109C-11D69
3Choose the two roots of $(3x + 4)(5x - 4) = 0$.
Ax = -4/3 or x = -4/5Bx = 4/3 or x = -4/5Cx = 4 or x = -4Dx = -4/3 or x = 4/5
4Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 + 7x - 3 = 0$.
A61B73C31D25
5Choose the two roots of $(3x + 2)(5x + 6) = 0$.
Ax = 2/3 or x = 6/5Bx = -2/3 or x = -6/5Cx = 2 or x = 6Dx = -2/3 or x = 6/5
6The equation $2x^2 + x + 1 = 0$ has how many real roots? Use the discriminant to justify your answer.
ATwo distinct real rootsBNo real rootsCOne repeated real rootDCannot be determined without solving
7Solve $3x^2 - 9x - 1 = 0$ using the quadratic formula.
Ax = 3.11 or x = -0.11Bx = 10.61 or x = 7.39Cx = 0.11 or x = -3.11Dx = 2.88 or x = 0.12
8The equation $x^2 + 6x - 5 = 0$ has how many real roots? Use the discriminant to justify your answer.
AOne repeated real rootBTwo distinct real rootsCNo real rootsDCannot be determined without solving
9Solve $3x^2 + 9x + 4 = 0$ using the quadratic formula.
Ax = -0.54 or x = -2.46Bx = 0.39 or x = -3.39Cx = -8.04 or x = -9.96Dx = 2.46 or x = 0.54
10The equation $2x^2 - 5x + 6 = 0$ has how many real roots? Use the discriminant to justify your answer.
ANo real rootsBOne repeated real rootCTwo distinct real rootsDCannot be determined without solving
11Solve $x^2 - 7x - 4 = 0$ using the quadratic formula.
Ax = 11.03 or x = 2.97Bx = 6.37 or x = 0.63Cx = 0.53 or x = -7.53Dx = 7.53 or x = -0.53
12Solve $3x^2 - 6x - 1 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{3 \pm 2\sqrt{3}}{3}$B$x = \dfrac{3 \pm 4\sqrt{3}}{3}$C$x = \dfrac{3 \pm 2\sqrt{3}}{4}$D$x = \dfrac{-3 \pm 2\sqrt{3}}{3}$
13A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{5 \pm \sqrt{25 - 4}}{2}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$x^2 - 5x + 1 = 0$B$2x^2 - 5x + 1 = 0$C$x^2 - 5x - 1 = 0$D$x^2 + 5x + 1 = 0$
14Solve $x^2 - 7x + 2 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{7 \pm \sqrt{41}}{2}$B$x = \dfrac{-7 \pm \sqrt{41}}{2}$C$x = \dfrac{7 \pm 2\sqrt{41}}{2}$D$x = 7 \pm \sqrt{41}$
15The equation $x^2 + 8x + k = 0$ has equal (repeated) roots.
Work out the value of $k$.
Ak = 60Bk = 16Ck = 64Dk = 4
How confident do you feel on this topic now?RedAmberGreen
The Quadratic Formula · MCQ assessment
Version B
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right123456789101112131415
/ 15
1Choose the two roots of $(x - 4)(2x + 5) = 0$.
Ax = -4 or x = 5Bx = 4 or x = -5/2Cx = -4 or x = 5/2Dx = 4 or x = 5/2
2Work out the value of the discriminant $b^2 - 4ac$ for $4x^2 + 7x + 6 = 0$.
A145B-89C-47D25
3Choose the two roots of $(3x + 5)(5x + 3) = 0$.
Ax = -5/3 or x = 3/5Bx = -5/3 or x = -3/5Cx = 5 or x = 3Dx = 5/3 or x = 3/5
4Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 + 5x + 2 = 0$.
A-11B9C41D17
5Choose the two roots of $(x - 2)(2x + 5) = 0$.
Ax = -2 or x = 5/2Bx = 2 or x = -5/2Cx = 2 or x = 5/2Dx = -2 or x = 5
6Solve $3x^2 - 5x - 5 = 0$ using the quadratic formula.
Ax = 0.70 or x = -2.37Bx = 6.54 or x = 3.46Cx = 4.74 or x = -1.41Dx = 2.37 or x = -0.70
7The equation $2x^2 - 4x + 2 = 0$ has how many real roots? Use the discriminant to justify your answer.
ATwo distinct real rootsBOne repeated real rootCNo real rootsDCannot be determined without solving
8Solve $x^2 + 5x + 2 = 0$ using the quadratic formula.
Ax = 4.56 or x = 0.44Bx = -0.44 or x = -4.56Cx = -2.94 or x = -7.06Dx = 0.37 or x = -5.37
9Solve $x^2 - 6x - 3 = 0$ using the quadratic formula.
Ax = 5.45 or x = 0.55Bx = 6.46 or x = -0.46Cx = 9.46 or x = 2.54Dx = 0.46 or x = -6.46
10The equation $3x^2 - 3x + 1 = 0$ has how many real roots? Use the discriminant to justify your answer.
AOne repeated real rootBNo real rootsCCannot be determined without solvingDTwo distinct real roots
11Solve $x^2 + 9x - 2 = 0$ using the quadratic formula.
Ax = 0.22 or x = -9.22Bx = -4.28 or x = -13.72Cx = -0.23 or x = -8.77Dx = 9.22 or x = -0.22
12Solve $3x^2 - 3x - 1 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{3 \pm \sqrt{21}}{3}$B$x = \dfrac{3 \pm \sqrt{21}}{6}$C$x = \dfrac{-3 \pm \sqrt{21}}{6}$D$x = \dfrac{3 \pm 2\sqrt{21}}{6}$
13A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{-9 \pm \sqrt{81 + 8}}{2}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$2x^2 + 9x - 2 = 0$B$x^2 + 9x + 2 = 0$C$x^2 - 9x - 2 = 0$D$x^2 + 9x - 2 = 0$
14The equation $x^2 + kx + 25 = 0$ has equal (repeated) roots.
Work out the possible values of $k$.
Ak = 5 or k = -5Bk = 10 or k = -10Ck = 100 or k = -100Dk = 10
15The equation $3x^2 + 6x + k = 0$ has equal (repeated) roots.
Work out the value of $k$.
Ak = 24Bk = 3Ck = 12Dk = 36
How confident do you feel on this topic now?RedAmberGreen
The Quadratic Formula · MCQ assessment
Version C
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right123456789101112131415
/ 15
1Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 + 9x - 4 = 0$.
A41B49C113D97
2Choose the two roots of $(2x + 5)(x - 4) = 0$.
Ax = 5 or x = -4Bx = 5/2 or x = -4Cx = -5/2 or x = 4Dx = -5/2 or x = -4
3Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 - 5x + 2 = 0$.
A-21B17C41D9
4Choose the two roots of $(3x + 2)(x + 2) = 0$.
Ax = -2/3 or x = -2Bx = 2/3 or x = 2Cx = -2/3 or x = 2Dx = 2 or x = 2
5Work out the value of the discriminant $b^2 - 4ac$ for $4x^2 + 5x + 2 = 0$.
A-7B17C57D-27
6Solve $3x^2 + 2x - 3 = 0$ using the quadratic formula.
Ax = 1.39 or x = -0.72Bx = 1.44 or x = -2.77Cx = -0.95 or x = -3.05Dx = 0.72 or x = -1.39
7The equation $2x^2 + 6x + 6 = 0$ has how many real roots? Use the discriminant to justify your answer.
ATwo distinct real rootsBNo real rootsCCannot be determined without solvingDOne repeated real root
8Solve $x^2 + 7x + 7 = 0$ using the quadratic formula.
Ax = 5.79 or x = 1.21Bx = -4.71 or x = -9.29Cx = -1.21 or x = -5.79Dx = 0.89 or x = -7.89
9The equation $x^2 + 2x + 1 = 0$ has how many real roots? Use the discriminant to justify your answer.
ATwo distinct real rootsBOne repeated real rootCCannot be determined without solvingDNo real roots
10Solve $x^2 - 7x - 5 = 0$ using the quadratic formula.
Ax = 11.15 or x = 2.85Bx = 6.19 or x = 0.81Cx = 7.65 or x = -0.65Dx = 0.65 or x = -7.65
11The equation $3x^2 + 2x + 5 = 0$ has how many real roots? Use the discriminant to justify your answer.
ANo real rootsBCannot be determined without solvingCOne repeated real rootDTwo distinct real roots
12Solve $3x^2 + 9x - 6 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{3 \pm \sqrt{17}}{2}$B$x = \dfrac{-3 \pm 2\sqrt{17}}{2}$C$x = \dfrac{-3 \pm \sqrt{17}}{3}$D$x = \dfrac{-3 \pm \sqrt{17}}{2}$
13A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{-5 \pm \sqrt{25 + 32}}{2}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$x^2 + 5x + 8 = 0$B$2x^2 + 5x - 8 = 0$C$x^2 - 5x - 8 = 0$D$x^2 + 5x - 8 = 0$
14Solve $3x^2 - 5x - 3 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{-5 \pm \sqrt{61}}{6}$B$x = \dfrac{5 \pm 2\sqrt{61}}{6}$C$x = \dfrac{5 \pm \sqrt{61}}{3}$D$x = \dfrac{5 \pm \sqrt{61}}{6}$
15The equation $x^2 + kx + 49 = 0$ has equal (repeated) roots.
Work out the possible values of $k$.
Ak = 14Bk = 196 or k = -196Ck = 7 or k = -7Dk = 14 or k = -14
How confident do you feel on this topic now?RedAmberGreen
The Quadratic Formula · MCQ assessment
Version D
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right123456789101112131415
/ 15
1Work out the value of the discriminant $b^2 - 4ac$ for $4x^2 - 8x + 6 = 0$.
A40B160C-32D-104
2Choose the two roots of $(3x + 4)(x - 1) = 0$.
Ax = -4/3 or x = -1Bx = 4/3 or x = -1Cx = -4/3 or x = 1Dx = 4 or x = -1
3Work out the value of the discriminant $b^2 - 4ac$ for $4x^2 - 2x - 4 = 0$.
A20B68C62D-60
4Choose the two roots of $(x + 1)(5x + 4) = 0$.
Ax = 1 or x = 4/5Bx = 1 or x = 4Cx = -1 or x = 4/5Dx = -1 or x = -4/5
5Work out the value of the discriminant $b^2 - 4ac$ for $3x^2 + 5x + 6 = 0$.
A1B97C-67D-47
6Solve $3x^2 + 6x - 3 = 0$ using the quadratic formula.
Ax = 0.41 or x = -2.41Bx = -4.59 or x = -7.41Cx = 2.41 or x = -0.41Dx = 0.83 or x = -4.83
7The equation $2x^2 - 4x + 5 = 0$ has how many real roots? Use the discriminant to justify your answer.
ACannot be determined without solvingBOne repeated real rootCTwo distinct real rootsDNo real roots
8Solve $x^2 + 9x + 6 = 0$ using the quadratic formula.
Ax = 0.62 or x = -9.62Bx = 8.27 or x = 0.73Cx = -0.73 or x = -8.27Dx = -5.23 or x = -12.77
9The equation $x^2 - 4x + 5 = 0$ has how many real roots? Use the discriminant to justify your answer.
AOne repeated real rootBTwo distinct real rootsCNo real rootsDCannot be determined without solving
10Solve $2x^2 + 7x - 6 = 0$ using the quadratic formula.
Ax = 0.71 or x = -4.21Bx = -4.54 or x = -9.46Cx = 4.21 or x = -0.71Dx = -1.50 or x = -2.00
11The equation $2x^2 + 7x - 5 = 0$ has how many real roots? Use the discriminant to justify your answer.
ATwo distinct real rootsBCannot be determined without solvingCNo real rootsDOne repeated real root
12A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{6 \pm \sqrt{36 + 8}}{4}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$4x^2 - 6x - 1 = 0$B$2x^2 - 6x + 1 = 0$C$2x^2 - 6x - 1 = 0$D$2x^2 + 6x - 1 = 0$
13Solve $2x^2 - 3x - 6 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{3 \pm \sqrt{57}}{2}$B$x = \dfrac{3 \pm 2\sqrt{57}}{4}$C$x = \dfrac{-3 \pm \sqrt{57}}{4}$D$x = \dfrac{3 \pm \sqrt{57}}{4}$
14A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{8 \pm \sqrt{64 - 20}}{2}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$x^2 + 8x + 5 = 0$B$2x^2 - 8x + 5 = 0$C$x^2 - 8x + 5 = 0$D$x^2 - 8x - 5 = 0$
15The equation $x^2 + kx + 4 = 0$ has equal (repeated) roots.
Work out the possible values of $k$.
Ak = 2 or k = -2Bk = 4Ck = 16 or k = -16Dk = 4 or k = -4
How confident do you feel on this topic now?RedAmberGreen
The Quadratic Formula · MCQ assessment
Version E
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right123456789101112131415
/ 15
1Work out the value of the discriminant $b^2 - 4ac$ for $3x^2 - 9x + 3 = 0$.
A45B69C-45D117
2Choose the two roots of $(x - 1)(5x - 3) = 0$.
Ax = 1 or x = 3/5Bx = -1 or x = -3Cx = -1 or x = -3/5Dx = 1 or x = -3/5
3Work out the value of the discriminant $b^2 - 4ac$ for $3x^2 + 2x - 5 = 0$.
A62B-56C24D64
4Choose the two roots of $(x + 4)(5x - 2) = 0$.
Ax = -4 or x = -2/5Bx = 4 or x = -2/5Cx = 4 or x = -2Dx = -4 or x = 2/5
5Work out the value of the discriminant $b^2 - 4ac$ for $3x^2 - 8x + 2 = 0$.
A56B88C-32D40
6The equation $x^2 - 5x + 1 = 0$ has how many real roots? Use the discriminant to justify your answer.
ANo real rootsBCannot be determined without solvingCOne repeated real rootDTwo distinct real roots
7Solve $x^2 + 6x + 6 = 0$ using the quadratic formula.
Ax = 0.87 or x = -6.87Bx = -4.27 or x = -7.73Cx = -1.27 or x = -4.73Dx = 4.73 or x = 1.27
8The equation $3x^2 - 6x - 5 = 0$ has how many real roots? Use the discriminant to justify your answer.
ATwo distinct real rootsBNo real rootsCCannot be determined without solvingDOne repeated real root
9Solve $x^2 + 2x - 4 = 0$ using the quadratic formula.
Ax = 3.24 or x = -1.24Bx = 0.24 or x = -4.24Cx = 1.24 or x = -3.24Dx = 0.74 or x = -3.74
10The equation $x^2 - 2x + 1 = 0$ has how many real roots? Use the discriminant to justify your answer.
ACannot be determined without solvingBOne repeated real rootCTwo distinct real rootsDNo real roots
11Solve $3x^2 + 6x - 1 = 0$ using the quadratic formula.
Ax = 2.15 or x = -0.15Bx = 0.15 or x = -2.15Cx = -4.85 or x = -7.15Dx = -0.18 or x = -1.82
12A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{8 \pm \sqrt{64 - 36}}{2}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$x^2 - 8x + 9 = 0$B$x^2 - 8x - 9 = 0$C$2x^2 - 8x + 9 = 0$D$x^2 + 8x + 9 = 0$
13Solve $3x^2 + 5x - 6 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{-5 \pm \sqrt{97}}{3}$B$x = \dfrac{5 \pm \sqrt{97}}{6}$C$x = \dfrac{-5 \pm 2\sqrt{97}}{6}$D$x = \dfrac{-5 \pm \sqrt{97}}{6}$
14A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{4 \pm \sqrt{16 + 8}}{4}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$2x^2 - 4x + 1 = 0$B$2x^2 - 4x - 1 = 0$C$2x^2 + 4x - 1 = 0$D$4x^2 - 4x - 1 = 0$
15The equation $x^2 + kx + 49 = 0$ has equal (repeated) roots.
Work out the possible values of $k$.
Ak = 7 or k = -7Bk = 14Ck = 196 or k = -196Dk = 14 or k = -14
How confident do you feel on this topic now?RedAmberGreen
The Quadratic Formula · MCQ assessment
Version F
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right123456789101112131415
/ 15
1Choose the two roots of $(x - 2)(2x - 5) = 0$.
Ax = 2 or x = 5/2Bx = -2 or x = -5/2Cx = 2 or x = -5/2Dx = -2 or x = -5
2Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 - 9x - 5 = 0$.
A101B31C121D41
3Choose the two roots of $(x + 2)(2x + 3) = 0$.
Ax = -2 or x = 3/2Bx = -2 or x = -3/2Cx = 2 or x = 3/2Dx = 2 or x = 3
4Work out the value of the discriminant $b^2 - 4ac$ for $3x^2 - x - 4 = 0$.
A47B49C-47D17
5Choose the two roots of $(2x - 3)(x + 2) = 0$.
Ax = 3/2 or x = -2Bx = -3/2 or x = 2Cx = -3 or x = 2Dx = 3/2 or x = 2
6Solve $3x^2 - 9x + 1 = 0$ using the quadratic formula.
Ax = 2.88 or x = 0.12Bx = 3.11 or x = -0.11Cx = -0.12 or x = -2.88Dx = 10.38 or x = 7.62
7The equation $2x^2 + 6x + 2 = 0$ has how many real roots? Use the discriminant to justify your answer.
ATwo distinct real rootsBNo real rootsCOne repeated real rootDCannot be determined without solving
8Solve $x^2 + 4x + 2 = 0$ using the quadratic formula.
Ax = 0.45 or x = -4.45Bx = 3.41 or x = 0.59Cx = -2.59 or x = -5.41Dx = -0.59 or x = -3.41
9The equation $2x^2 - 2x + 5 = 0$ has how many real roots? Use the discriminant to justify your answer.
ATwo distinct real rootsBOne repeated real rootCNo real rootsDCannot be determined without solving
10Solve $3x^2 - 8x - 2 = 0$ using the quadratic formula.
Ax = 2.90 or x = -0.23Bx = 0.23 or x = -2.90Cx = 2.39 or x = 0.28Dx = 9.56 or x = 6.44
11The equation $x^2 - 4x + 4 = 0$ has how many real roots? Use the discriminant to justify your answer.
ACannot be determined without solvingBTwo distinct real rootsCNo real rootsDOne repeated real root
12Solve $3x^2 + 8x - 6 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{-4 \pm \sqrt{34}}{4}$B$x = \dfrac{-4 \pm 2\sqrt{34}}{3}$C$x = \dfrac{-4 \pm \sqrt{34}}{3}$D$x = \dfrac{4 \pm \sqrt{34}}{3}$
13A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{-9 \pm \sqrt{81 - 40}}{2}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$x^2 + 9x - 10 = 0$B$x^2 - 9x + 10 = 0$C$2x^2 + 9x + 10 = 0$D$x^2 + 9x + 10 = 0$
14Solve $3x^2 + 6x - 2 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{-3 \pm 2\sqrt{15}}{3}$B$x = \dfrac{-3 \pm \sqrt{15}}{3}$C$x = \dfrac{-3 \pm \sqrt{15}}{4}$D$x = \dfrac{3 \pm \sqrt{15}}{3}$
15The equation $x^2 + kx + 49 = 0$ has equal (repeated) roots.
Work out the possible values of $k$.
Ak = 196 or k = -196Bk = 7 or k = -7Ck = 14 or k = -14Dk = 14
How confident do you feel on this topic now?RedAmberGreen
The Quadratic Formula · MCQ assessment
Version G
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right123456789101112131415
/ 15
1Choose the two roots of $(2x + 3)(x - 6) = 0$.
Ax = 3 or x = -6Bx = -3/2 or x = 6Cx = -3/2 or x = -6Dx = 3/2 or x = -6
2Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 - 6x - 1 = 0$.
A28B40C44D2
3Choose the two roots of $(x - 4)(2x + 3) = 0$.
Ax = 4 or x = 3/2Bx = 4 or x = -3/2Cx = -4 or x = 3/2Dx = -4 or x = 3
4Work out the value of the discriminant $b^2 - 4ac$ for $3x^2 - 3x + 4 = 0$.
A-51B-7C57D-39
5Choose the two roots of $(2x + 1)(5x - 4) = 0$.
Ax = 1 or x = -4Bx = -1/2 or x = -4/5Cx = 1/2 or x = -4/5Dx = -1/2 or x = 4/5
6Solve $2x^2 - 7x - 7 = 0$ using the quadratic formula.
Ax = 8.62 or x = -1.62Bx = 0.81 or x = -4.31Cx = 9.56 or x = 4.44Dx = 4.31 or x = -0.81
7The equation $3x^2 + 7x - 5 = 0$ has how many real roots? Use the discriminant to justify your answer.
ATwo distinct real rootsBNo real rootsCCannot be determined without solvingDOne repeated real root
8Solve $x^2 - 7x - 5 = 0$ using the quadratic formula.
Ax = 7.65 or x = -0.65Bx = 11.15 or x = 2.85Cx = 6.19 or x = 0.81Dx = 0.65 or x = -7.65
9The equation $x^2 - 4x + 6 = 0$ has how many real roots? Use the discriminant to justify your answer.
ATwo distinct real rootsBCannot be determined without solvingCOne repeated real rootDNo real roots
10Solve $2x^2 + 7x - 1 = 0$ using the quadratic formula.
Ax = -5.11 or x = -8.89Bx = -0.15 or x = -3.35Cx = 3.64 or x = -0.14Dx = 0.14 or x = -3.64
11The equation $x^2 - 3x + 6 = 0$ has how many real roots? Use the discriminant to justify your answer.
ANo real rootsBTwo distinct real rootsCOne repeated real rootDCannot be determined without solving
12A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{5 \pm \sqrt{25 - 8}}{4}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$2x^2 - 5x - 1 = 0$B$2x^2 + 5x + 1 = 0$C$2x^2 - 5x + 1 = 0$D$4x^2 - 5x + 1 = 0$
13Solve $x^2 - 4x - 3 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = 2 \pm 2\sqrt{7}$B$x = \dfrac{2 \pm \sqrt{7}}{2}$C$x = -2 \pm \sqrt{7}$D$x = 2 \pm \sqrt{7}$
14A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{8 \pm \sqrt{64 + 20}}{2}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$x^2 + 8x - 5 = 0$B$2x^2 - 8x - 5 = 0$C$x^2 - 8x + 5 = 0$D$x^2 - 8x - 5 = 0$
15The equation $x^2 + kx + 36 = 0$ has equal (repeated) roots.
Work out the possible values of $k$.
Ak = 12Bk = 6 or k = -6Ck = 12 or k = -12Dk = 144 or k = -144
How confident do you feel on this topic now?RedAmberGreen
The Quadratic Formula · MCQ assessment
Version H
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right123456789101112131415
/ 15
1Work out the value of the discriminant $b^2 - 4ac$ for $4x^2 - 6x - 2 = 0$.
A26B44C68D4
2Choose the two roots of $(3x + 1)(x + 2) = 0$.
Ax = -1/3 or x = -2Bx = 1 or x = 2Cx = 1/3 or x = 2Dx = -1/3 or x = 2
3Work out the value of the discriminant $b^2 - 4ac$ for $3x^2 - 7x + 2 = 0$.
A-31B25C41D73
4Choose the two roots of $(2x + 1)(x + 6) = 0$.
Ax = -1/2 or x = -6Bx = 1/2 or x = 6Cx = -1/2 or x = 6Dx = 1 or x = 6
5Work out the value of the discriminant $b^2 - 4ac$ for $4x^2 - 9x - 1 = 0$.
A97B7C85D65
6The equation $x^2 - 3x + 5 = 0$ has how many real roots? Use the discriminant to justify your answer.
ANo real rootsBCannot be determined without solvingCTwo distinct real rootsDOne repeated real root
7Solve $2x^2 - 8x + 4 = 0$ using the quadratic formula.
Ax = 4.45 or x = -0.45Bx = 9.41 or x = 6.59Cx = 3.41 or x = 0.59Dx = -0.59 or x = -3.41
8The equation $3x^2 - 6x + 3 = 0$ has how many real roots? Use the discriminant to justify your answer.
ACannot be determined without solvingBOne repeated real rootCNo real rootsDTwo distinct real roots
9Solve $x^2 + 5x - 3 = 0$ using the quadratic formula.
Ax = 5.54 or x = -0.54Bx = -1.96 or x = -8.04Cx = -0.70 or x = -4.30Dx = 0.54 or x = -5.54
10The equation $x^2 + 2x + 1 = 0$ has how many real roots? Use the discriminant to justify your answer.
ANo real rootsBOne repeated real rootCCannot be determined without solvingDTwo distinct real roots
11Solve $x^2 + 7x - 7 = 0$ using the quadratic formula.
Ax = 7.89 or x = -0.89Bx = -1.21 or x = -5.79Cx = -2.61 or x = -11.39Dx = 0.89 or x = -7.89
12A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{-9 \pm \sqrt{81 - 24}}{2}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$x^2 - 9x + 6 = 0$B$2x^2 + 9x + 6 = 0$C$x^2 + 9x + 6 = 0$D$x^2 + 9x - 6 = 0$
13Solve $x^2 + 8x - 3 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = -4 \pm 2\sqrt{19}$B$x = \dfrac{-4 \pm \sqrt{19}}{2}$C$x = -4 \pm \sqrt{19}$D$x = 4 \pm \sqrt{19}$
14Solve $2x^2 + 6x - 4 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{3 \pm \sqrt{17}}{2}$B$x = \dfrac{-3 \pm \sqrt{17}}{2}$C$x = \dfrac{-3 \pm \sqrt{17}}{3}$D$x = \dfrac{-3 \pm 2\sqrt{17}}{2}$
15The equation $x^2 + kx + 36 = 0$ has equal (repeated) roots.
Work out the possible values of $k$.
Ak = 12 or k = -12Bk = 6 or k = -6Ck = 12Dk = 144 or k = -144
How confident do you feel on this topic now?RedAmberGreen
The Quadratic Formula · MCQ assessment
Version I
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right123456789101112131415
/ 15
1Choose the two roots of $(x + 2)(2x + 3) = 0$.
Ax = 2 or x = 3/2Bx = -2 or x = 3/2Cx = -2 or x = -3/2Dx = 2 or x = 3
2Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 - 8x - 3 = 0$.
A88B40C76D16
3Choose the two roots of $(x - 3)(5x + 3) = 0$.
Ax = -3 or x = 3/5Bx = 3 or x = 3/5Cx = 3 or x = -3/5Dx = -3 or x = 3
4Work out the value of the discriminant $b^2 - 4ac$ for $3x^2 + 5x - 1 = 0$.
A17B13C29D37
5Choose the two roots of $(2x + 3)(x + 2) = 0$.
Ax = -3/2 or x = 2Bx = -3/2 or x = -2Cx = 3 or x = 2Dx = 3/2 or x = 2
6Solve $x^2 - 6x + 3 = 0$ using the quadratic formula.
Ax = -0.55 or x = -5.45Bx = 8.45 or x = 3.55Cx = 5.45 or x = 0.55Dx = 6.46 or x = -0.46
7The equation $3x^2 - 5x - 6 = 0$ has how many real roots? Use the discriminant to justify your answer.
ANo real rootsBOne repeated real rootCCannot be determined without solvingDTwo distinct real roots
8Solve $x^2 - x - 5 = 0$ using the quadratic formula.
Ax = 2.29 or x = -2.29Bx = 3.29 or x = -1.29Cx = 2.79 or x = -1.79Dx = 1.79 or x = -2.79
9The equation $3x^2 - 6x - 5 = 0$ has how many real roots? Use the discriminant to justify your answer.
ACannot be determined without solvingBNo real rootsCTwo distinct real rootsDOne repeated real root
10Solve $x^2 + 7x + 3 = 0$ using the quadratic formula.
Ax = -3.96 or x = -10.04Bx = 6.54 or x = 0.46Cx = 0.41 or x = -7.41Dx = -0.46 or x = -6.54
11The equation $2x^2 + 6x + 5 = 0$ has how many real roots? Use the discriminant to justify your answer.
AOne repeated real rootBTwo distinct real rootsCNo real rootsDCannot be determined without solving
12Solve $2x^2 + 3x - 4 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{-3 \pm \sqrt{41}}{2}$B$x = \dfrac{-3 \pm \sqrt{41}}{4}$C$x = \dfrac{-3 \pm 2\sqrt{41}}{4}$D$x = \dfrac{3 \pm \sqrt{41}}{4}$
13A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{-4 \pm \sqrt{16 + 8}}{2}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$2x^2 + 4x - 2 = 0$B$x^2 + 4x - 2 = 0$C$x^2 - 4x - 2 = 0$D$x^2 + 4x + 2 = 0$
14Solve $x^2 - 4x - 2 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = 2 \pm \sqrt{6}$B$x = -2 \pm \sqrt{6}$C$x = \dfrac{2 \pm \sqrt{6}}{2}$D$x = 2 \pm 2\sqrt{6}$
15The equation $x^2 + kx + 25 = 0$ has equal (repeated) roots.
Work out the possible values of $k$.
Ak = 10 or k = -10Bk = 10Ck = 5 or k = -5Dk = 100 or k = -100
How confident do you feel on this topic now?RedAmberGreen
The Quadratic Formula · MCQ assessment
Version J
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right123456789101112131415
/ 15
1Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 - 2x + 1 = 0$.
A12B-10C0D-4
2Choose the two roots of $(x + 6)(2x + 5) = 0$.
Ax = 6 or x = 5/2Bx = -6 or x = -5/2Cx = -6 or x = 5/2Dx = 6 or x = 5
3Work out the value of the discriminant $b^2 - 4ac$ for $3x^2 - x - 5 = 0$.
A-59B61C21D59
4Choose the two roots of $(3x - 4)(2x - 3) = 0$.
Ax = -4/3 or x = -3/2Bx = 4/3 or x = -3/2Cx = -4 or x = -3Dx = 4/3 or x = 3/2
5Work out the value of the discriminant $b^2 - 4ac$ for $4x^2 - x + 3 = 0$.
A49B-47C-11D-49
6Solve $3x^2 + 5x + 1 = 0$ using the quadratic formula.
Ax = 1.43 or x = 0.23Bx = -0.23 or x = -1.43Cx = 0.18 or x = -1.85Dx = -4.40 or x = -5.60
7The equation $3x^2 - 6x + 3 = 0$ has how many real roots? Use the discriminant to justify your answer.
ANo real rootsBCannot be determined without solvingCOne repeated real rootDTwo distinct real roots
8Solve $3x^2 + x - 5 = 0$ using the quadratic formula.
Ax = 1.14 or x = -1.47Bx = 2.27 or x = -2.94Cx = 1.47 or x = -1.14Dx = 0.30 or x = -2.30
9The equation $2x^2 - 2x - 6 = 0$ has how many real roots? Use the discriminant to justify your answer.
ATwo distinct real rootsBCannot be determined without solvingCOne repeated real rootDNo real roots
10Solve $x^2 + 9x + 2 = 0$ using the quadratic formula.
Ax = 0.22 or x = -9.22Bx = -4.73 or x = -13.27Cx = -0.23 or x = -8.77Dx = 8.77 or x = 0.23
11The equation $x^2 + 3x + 4 = 0$ has how many real roots? Use the discriminant to justify your answer.
ATwo distinct real rootsBCannot be determined without solvingCNo real rootsDOne repeated real root
12Solve $2x^2 + 5x - 5 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{-5 \pm \sqrt{65}}{4}$B$x = \dfrac{-5 \pm \sqrt{65}}{2}$C$x = \dfrac{-5 \pm 2\sqrt{65}}{4}$D$x = \dfrac{5 \pm \sqrt{65}}{4}$
13A student uses the quadratic formula to solve an equation and correctly gets $x = \dfrac{-6 \pm \sqrt{36 - 24}}{4}$.
Work out the equation, in the form $ax^2 + bx + c = 0$.
A$4x^2 + 6x + 3 = 0$B$2x^2 + 6x + 3 = 0$C$2x^2 - 6x + 3 = 0$D$2x^2 + 6x - 3 = 0$
14Solve $x^2 + 8x - 5 = 0$ using the quadratic formula.
Give your answers in surd form.
A$x = \dfrac{-4 \pm \sqrt{21}}{2}$B$x = -4 \pm 2\sqrt{21}$C$x = -4 \pm \sqrt{21}$D$x = 4 \pm \sqrt{21}$
15The equation $x^2 + kx + 36 = 0$ has equal (repeated) roots.
Work out the possible values of $k$.
Ak = 12Bk = 144 or k = -144Ck = 6 or k = -6Dk = 12 or k = -12
How confident do you feel on this topic now?RedAmberGreen
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