# How do you find the roots of x^3+x^2-17x+15=0?

Sep 23, 2016

The roots are: $x = 1$, $x = - 5$ and $x = 3$

#### Explanation:

${x}^{3} + {x}^{2} - 17 x + 15 = 0$

Note that the sum of the coefficients is $0$. That is:

$1 + 1 - 17 + 15 = 0$

So $x = 1$ is a root and $\left(x - 1\right)$ a factor:

$0 = {x}^{3} + {x}^{2} - 17 x + 15$

$\textcolor{w h i t e}{0} = \left(x - 1\right) \left({x}^{2} + 2 x - 15\right)$

Then note that $5 \cdot 3 = 15$ and $5 - 3 = 2$, so

${x}^{2} + 2 x - 15 = \left(x + 5\right) \left(x - 3\right)$

So the other two roots are $x = - 5$ and $x = 3$