# How do you use the rational root theorem to find the roots of F(x) = 4x^3 - 6x^2 + 9x + 10?

Sep 11, 2015

You can't. The polynomial function has no rational zeros.

#### Explanation:

$F \left(x\right) = 4 {x}^{3} - 6 {x}^{2} + 9 x + 10$

Possible rational zeros are:

$\pm 1 , \pm 2 , \pm 5 , \pm 10 , \pm \frac{1}{2} , \pm \frac{5}{2} , \pm \frac{1}{4} , \pm \frac{5}{4}$

None of these is a zero, therefore there are no rational zeros.