Quadratic Formula and Discriminant

• r = -4, r = 2/3

• r = 4, r = -2/3

• r = -2, r = 4/3

• r = 2, r = -4/3

Answer explanation

Using the quadratic formula r = (-b ± √(b²-4ac)) / 2a with a=3, b=10, c=-8, we find the roots. The solutions simplify to r = -4 and r = 2/3, matching the correct choice.

• x = 8/5, x = 2

• x = 2/5, x = 8

• x = 4, x = 4/5

• x = 16/5, x = 1

Answer explanation

Using the quadratic formula x = (-b ± √(b²-4ac)) / 2a with a=5, b=-24, c=16, we find the discriminant is 576. This gives solutions x = (24 ± 24) / 10, resulting in x = 8/5 and x = 2, which matches the correct choice.

• 1 or 1/6

• 3/2 or 1

• 3 or 2/3

• 2 or 3/2

Answer explanation

To solve the equation 6b^2 - 11b + 3 = 0 using the quadratic formula, we find b = (11 ± √(121 - 72)) / 12. This simplifies to b = 1 or b = 1/6, making the correct answer 1 or 1/6.

• 57

• -105

• 105

• -57

Answer explanation

To find the discriminant of the quadratic equation -2x^2 + 9x + 3 = 0, use the formula D = b^2 - 4ac. Here, a = -2, b = 9, c = 3. Thus, D = 9^2 - 4(-2)(3) = 81 + 24 = 105. Therefore, the correct answer is 105.

• -81

• 81

• 63

• -63

Answer explanation

The discriminant of a quadratic equation ax^2 + bx + c is given by D = b^2 - 4ac. Here, a = 9, b = 3, c = 2. Thus, D = 3^2 - 4(9)(2) = 9 - 72 = -63. Therefore, the correct answer is -63.

• 36

• 92

• -92

• -36

Answer explanation

To find the discriminant of the equation -x^2 - 8x - 7 = 0, use the formula D = b^2 - 4ac. Here, a = -1, b = -8, c = -7. Thus, D = (-8)^2 - 4(-1)(-7) = 64 - 28 = 36. The correct answer is 36.

• 580

• 484

• 256

• 144

Answer explanation

To find the discriminant of the equation -3x^2 + 4x + 53 = 6, first rewrite it as -3x^2 + 4x + 47 = 0. The discriminant is given by b^2 - 4ac. Here, a = -3, b = 4, c = 47. Thus, D = 4^2 - 4(-3)(47) = 16 + 564 = 580.

• -16

• 49

• 121

• 64

Answer explanation

To find the discriminant, first rewrite the equation as x^2 + 16x + 68 = 0. The discriminant is given by b^2 - 4ac, where a=1, b=16, c=68. Thus, D = 16^2 - 4(1)(68) = 256 - 272 = -16. The correct answer is -16.

• x = 3, x = 1/2

• x = 1, x = 3/2

• x = 1/3, x = 3

• x = 3/2, x = 1/3

Answer explanation

Using the quadratic formula x = (-b ± √(b²-4ac)) / 2a with a=2, b=-7, c=3, we find the discriminant is 25. Thus, the solutions are x = (7 ± 5)/4, giving x = 3 and x = 1/2. The correct choice is x = 3, x = 1/2.

• 36

• 9

• 16

• 0

Answer explanation

To find the discriminant of the quadratic equation 4x^2 - 12x + 9 = 0, use the formula D = b^2 - 4ac. Here, a = 4, b = -12, c = 9. Thus, D = (-12)^2 - 4(4)(9) = 144 - 144 = 0. The correct answer is 0.