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 irrational solutions.
There are two irrational solutions.

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

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

There are two rational solutions.

Answer 1

Divide by −4: x^2 + 6x + 9 = 0. The discriminant is b^2 − 4ac = 36 − 36 = 0, so there is a repeated real root. By the quadratic formula x = (−6 ± 0)/2 = −3.

Thus the solution set is two identical solutions (x = −3, double root).