Question

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 non-real solutions.
There are two non-real solutions.

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

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

There are two rational solutions.

Answer 1

Use the quadratic formula or compute the discriminant.

Divide by −4: x^2 + 6x + 9 = 0, which is (x + 3)^2 = 0.
Or with the discriminant: D = b^2 − 4ac = (−24)^2 − 4(−4)(−36) = 576 − 576 = 0.

Thus there is a repeated real root x = −3 (a double root).
Correct choice: There are two identical solutions.