Question

Which of the following quadratic equations has two complex solutions? Select all that apply

a)y = 2(x - 4)^2 + 5
b)y = -2x + 16x - 37
c)y = -5(x^2 - 3)
d)y = -x^2 + 4x - 5
e)y = -4(x + 2)^2 - 3

Answer 1

None of the given quadratic equations have two complex solutions.

Step-by-step explanation:

A quadratic equation has two complex solutions if the discriminant, b² - 4ac, is negative. Let's check each quadratic equation to see which ones have two complex solutions:

a) y = 2(x - 4)² + 5
The discriminant is 0, so it has two equal real solutions. Not a complex solution.

b) y = -2x + 16x - 37
The discriminant is positive, so it has two real and distinct solutions. Not a complex solution.

c) y = -5(x² - 3)
The discriminant is 0, so it has two equal real solutions. Not a complex solution.

d) y = -x² + 4x - 5
The discriminant is positive, so it has two real and distinct solutions. Not a complex solution.

e) y = -4(x + 2)² - 3
The discriminant is 0, so it has two equal real solutions. Not a complex solution.

Therefore, none of the given quadratic equations have two complex solutions. The correct answer is none of the above.