Question

Which of the following statements is true

regarding the solutions to the quadratic
equation 5x^2 + 6x + 2 = 0?

A. This quadratic equation has no solutions.

B. This quadratic equation has two real solutions.

C. This quadratic equation has exactly one real solution.

D. This quadratic equation two complex solutions.

Answer 1

D. This quadratic equation two complex solutions.

Explanation:

`5x^2 +6x +2= 0\\`

Equating it with

`ax^2 +bx +c= 0\\`

a = 5, b = 6, c = 2

`b^2 -4ac\\= 6^2 - 4* 5* 2\\</p><p>= 36-40\\</p><p>b^2 -4ac= - 4\\</p><p>`

`\because b^2 -4ac` is negative.

Therefore, this quadratic equation two complex solutions.