# How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given f(x)=10x^3-17x^2-7x+2?

Nov 29, 2016

#### Answer:

$- \frac{1}{2} , \frac{1}{5} \mathmr{and} 2$

#### Explanation:

The number of changes in the signs of coefficients of f(x) is 2. So thr

limit for the number of positive roots is 2.

Likewise, this number for f(-x) is 1. So, the number of negative roots

is either 0 or 1.

As f(2) = 0, 2 is a zero of f, and so,

$\left(x - 2\right)$ is a factor of f. Easily, the other factor is

$10 {x}^{2} + 3 x - 1$. The zeros of this quadratic are $- \frac{1}{2} \mathmr{and} \frac{1}{5}$.