Question

The function below has at least one rational root. Find the factors of the polynomials

f(x) = x²-2x+6
A. (x-√2)(x+√2)(x-3)
B. (x²-2)(x-3)
C. (x-1)(x²-2x-8)
D. (x-1)(x+2)(x-4)

Answer 1

The polynomial function f(x) = x² - 2x + 6 has no rational root

How to determine the factors of the polynomial

From the question, we have the following parameters that can be used in our computation:

f(x) = x² - 2x + 6

We calculate the discriminant to calculate if the polynomial has a factor using

d = b² - 4ac

Where

a = 1, b = -2 and c = 6

Substitute the known values into the equation

d = (-2)² - 4 * 1 * 6

Evaluate

d = -20

This value is less than 0

It means that it has no rational root