A set of questions, with answers, on quadratic equations are presented. The answers to the questions are at the bottom of the page and the solutions with full explanations to these questions are also included.

What are the two solutions to the quadratic equations 2 x^{2} + 3x - 2 = 0?

A) -2 , 3
B) -2 , -1/2
C) 2 , -1/2
D) -2 , 1/2
E) -1/2 , -2

What is the sum of the two solutions to the quadratic equation (x + 4)(x - 3) = 7

A) -1
B) -2
C) 1
D) 2
E) 3

What is the product of the two solutions to the quadratic equation (x - 2)(x - 6) = -3

A) 12
B) -12
C) 15
D) -3
E) 3

Find all values of m for which the quadratic equation x^{2} + 2 x - 2 m = 0 have no real solutions.

A) m = 0
B) m = -2
C) m < - 4
D) m = 1 / 2
E) m < -1 / 2

Find all values of m for which the quadratic equation 2x^{2} + 3 x - m + 2 = 0 have two distinct real solutions.

A) m > 0
B) m = 7
C) m > 7 / 8
D) m < -7 / 8
E) m = 7 / 8

Which of these quadratic equations has two real solutions greater than zero?

A) x^{2} + x = 0
B) 2 x^{2} - 10 x = 28
C) - x^{2} + 4 x + 5 = 0
D) -3 x^{2} - 9 = - 12 x
E) -3 x^{2} - 6 x + 24 = 0

Which of these quadratic equations has two real solutions whose product is greater than zero?

A) - x^{2} - 2x = - 8
B) x^{2} + 9 x = - 18
C) - x^{2} = - 6 + x
D) x^{2} = 4 x
E) x^{2} - 3 x = 4

b and c in the quadratic equation x^{2} + bx + c = 0 are real numbers. Find b and c so that the given equation has two solutions x = -1/4 and x = 1/2.

A) b = - 1 / 4 , c = - 1 / 8
B) b = - 1 , c = - 1
C) b = 1 / 4, c = -1
D) b = 1 / 4, c = 1 / 8
E) b = 4, c = 8

b and c in the quadratic equation - x^{2} + bx + c = 0 are real numbers. Find b and c so that the given equation has two solutions whose sum is equal to 6 and whose product is equal to 8.

A) b = 6 , c = 8
B) b = -6 , c = 8
C) b = 8 , c = -6
D) b = 6 , c = -8
E) b = -8 , c = 6

Which of these pairs of quadratic equations have the same solutions?(equivalent equations)

A) x^{2} - 1 = 0 and x^{2} = - 1
B) - x^{2} + x = - 6 and x^{2} - 2x = 3
C) x^{2} - 5x + 6 = 0 and - x^{2} - 5x - 6 = 0
D) x^{2} = 2x and x^{2} + 2x = 0
E) x^{2} + x - 2 = 0 and - 2 x^{2} -2x + 4 = 0