Root me this

Algebra Level 2

Consider the equation:

$f(x) =x^3 +x^2 - 8x + 1$

Does this equation have a root between 2 and 3?

No Yes Cannot be determined

2 solutions

Denton Young
Sep 1, 2019

$f(2) = -3$

$f(3) = 13$

Since $f(x)$ is a polynomial function and thus continuous, by Bolzano's theorem it must have a root between 2 and 3.

Hi Bye
Sep 5, 2019

Since $f(2)$ and $f(3)$ have opposite signs, $\boxed{\text{Yes}},$ there must be a root between $2$ and $3$ .