Mathematics Quiz 09

a and b in the quadratic equation x2 + ax + b = 0 are real numbers. Find a and b so that the given equation has two solutions x = -1/4 and x = 1/2.

a = - 1 / 4 , b = - 1 / 8

a = 4 , b = 8

a = 1 , b = 1

a = - 1 , b = - 1

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

-3 x2 - 6 x + 24 = 0

-3 x2 - 9 = - 12 x

2 x2 - 10 x = 28

x2 + x = 0

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

- x2 + x = - 6 and x2 - 2x = 3

x2 + x - 2 = 0 and - 2 x2 -2x + 4 = 0

x2 = 2x and x2 + 2x = 0

x2 - 1 = 0 and x2 = - 1

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

- x2 = - 6 + x

- x2 - 2x = - 8

x2 = 4 x

x2 + 9 x = - 18

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

-2

2

1

-1

Find all values of m for which the quadratic equation 2x2 + 3 x - m + 2 = 0 have two distinct real solutions

m > 7/8

m = 7

m > 0

m < -7/8

What are the two solutions to the quadratic equations 2 x2 + 3x - 2 = 0?

-2 , 1/2

-2 , 3

2 , 1/2

-2 , -1/2

Find all values of m for which the quadratic equation x2 + 2 x - 2 m = 0 have no real solutions.

m < -1 / 2

m = -2

m = 0

m = 1 / 2

a and b in the quadratic equation - x2 + ax + b = 0 are real numbers. Find a and b so that the given equation has two solutions whose sum is equal to 6 and whose product is equal to 8

a = 6 , b = 8

a = -6 , b = -8

a = -6 , b = 8

a = 6 , b = -8

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

15

-12

3

12