Question

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?

Answer 1

Answer:

The answer is B  " +/- 1/5 , +/- 1 , +/- 11/5 , +/- 11 "

Answer 2

We will determine the roots of the given equation $5x^3-7x+11=0$ by rational root theorem.

Rational root theorem states:

"If P(x) is a polynomial with integer coefficients, then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).Then all the possible values of $\frac{p}{q}$ are the factors of the given polynomial".

Therefore, the given equation is:

$5x^3-7x+11=0$

The factors of the leading coefficient of $x^3$ = q = $\pm 1, \pm 5$

The factors of the constant = p = $\pm 1, \pm 11$

So, the possible values of $\frac{p}{q} = \pm 1 , \frac{\pm 1}{\pm 5},{\pm 11}, \frac{\pm 11}{\pm 5}$.

Therefore, the roots of the given polynomial are $\frac{p}{q} = \pm 1 , \frac{\pm 1}{\pm 5},{\pm 11}, \frac{\pm 11}{\pm 5}$.