# How do you find all zeros with multiplicities of f(x)=-17x^3+5x^2+34x-10?

Jul 14, 2017

The zeros are $x = \frac{5}{17} , x = \sqrt{2} , x = - \sqrt{2}$

#### Explanation:

$f \left(x\right) = - 17 {x}^{3} + 5 {x}^{2} + 34 x - 10$ or

$f \left(x\right) = - 17 {x}^{3} + 34 x + 5 {x}^{2} - 10$ or

$f \left(x\right) = - 17 x \left({x}^{2} - 2\right) + 5 \left({x}^{2} - 2\right)$ or

$f \left(x\right) = \left({x}^{2} - 2\right) \left(- 17 x + 5\right)$ or

$f \left(x\right) = \left(x + \sqrt{2}\right) \left(x - \sqrt{2}\right) \left(- 17 x + 5\right)$

$f \left(x\right) = 0$ When $\left(x + \sqrt{2}\right) = 0 \mathmr{and} x = - \sqrt{2}$ ,

$\left(x - \sqrt{2}\right) = 0 \mathmr{and} x = \sqrt{2}$ and $\left(- 17 x + 5\right) = 0 \mathmr{and} 17 x = 5 \mathmr{and} x = \frac{5}{17}$

The zeros are $x = \frac{5}{17} , x = \sqrt{2} , x = - \sqrt{2}$ [Ans]