Question

Show that the Fundamental Theorem of Algebra is true for the quadratic polynomial −4x2−24x−36=0
by using the quadratic formula. Which of the following statements accurately describes the solution set?

(1 point)
Responses

There are two identical solutions.
There are two identical solutions.

There are two rational solutions.
There are two rational solutions.

There are two irrational solutions.
There are two irrational solutions.

There are two non-real solutions.

Answer 1

Divide both sides by −4 to get x^2 + 6x + 9 = 0.
Discriminant Δ = 6^2 − 4·1·9 = 36 − 36 = 0, so the quadratic formula gives x = −6/(2) = −3 (double root).

Thus there are two identical solutions.