Question

When using the rational root theorem, which of the following is a possible root of the polynomial function below?

F(x) = 2x² - 4x +9

A. 5
B. 3
C. 4
D. 2

Answer 1

Using the quadratic formula, it's determined that the quadratic function F(x) = 2x² - 4x + 9 has no real roots because the discriminant is negative. Thus, none of the provided options are possible roots for this polynomial.

Step-by-step explanation:

The question refers to finding a possible root of the polynomial function F(x) = 2x² - 4x + 9 using the rational root theorem.

Instead, for quadratic equations of the form ax² + bx + c = 0, we usually use the quadratic formula to find the roots.

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). We can apply this formula to find the roots of our polynomial:

Let's calculate the discriminant (√(b² - 4ac)):

√((-4)² - 4(2)(9)) = √(16 - 72) = √(-56)

Since the discriminant is negative, this means the quadratic function has no real roots, so none of the provided options A. 5, B. 3, C. 4, D. 2 are possible roots for F(x).