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 non-real solutions There are two non-real solutions There are two irrational solutions
To solve the quadratic polynomial −4x^2 − 24x − 36 = 0 using the quadratic formula, we first identify the coefficients:
a = -4
b = -24
c = -36
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the coefficients into the formula, we have:
x = (-(-24) ± √((-24)^2 - 4(-4)(-36))) / (2(-4))
Simplifying the equation further:
x = (24 ± √(576 - 576)) / (-8)
x = (24 ± √0) / (-8)
x = (24 ± 0) / (-8)
Since the discriminant (√(b^2 - 4ac)) is 0, both solutions are identical. Therefore, the correct statement is:
There are two identical solutions.