# How do you find a polynomial function that has zeros 0, 2, 5?

##### 1 Answer
Feb 10, 2017

$f \left(x\right) = {x}^{3} - 7 {x}^{2} + 10 x$

#### Explanation:

Let $f \left(x\right)$ be the required polynomial.

We are told that $f \left(x\right) = 0$ for $x = \left\{0 , 2 , 5\right\}$

Thus: $x , \left(x - 2\right) , \left(x - 5\right)$ must be factors of $f \left(x\right)$

$\therefore f \left(x\right) = x \left(x - 2\right) \left(x - 5\right)$

$= x \left({x}^{2} - 7 x + 10\right)$

$= {x}^{3} - 7 {x}^{2} + 10 x$