Show that the Fundamental Theorem of Algebra is true for the quadratic polynomial −2x2+4x−9=0 by using the quadratic formula. Which of the following statements accurately describes the solution set?(1 point) Responses There are two rational solutions. There are two rational solutions. 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.
To find the solutions of the quadratic polynomial −2x^2+4x−9=0 using the quadratic formula, we can use the formula:
x = (-b ± sqrt(b^2 - 4ac))/(2a)
For the given quadratic polynomial, the coefficients are:
a = -2, b = 4, c = -9.
Plugging these values into the quadratic formula, we have:
x = (-4 ± sqrt(4^2 - 4(-2)(-9))) / (2(-2))
Simplifying further:
x = (-4 ± sqrt(16 - 72)) / (-4)
x = (-4 ± sqrt(-56)) / (-4)
Since the discriminant (b^2 - 4ac) is negative (-56 in this case), the quadratic formula will result in two non-real solutions.
Therefore, the statement "There are two non-real solutions" accurately describes the solution set.