# How do you find a polynomial function that has zeros -4, 5?

Dec 8, 2017

$p \left(x\right) = {x}^{2} - x - 20$

#### Explanation:

$\text{given the zeros of a polynomial "x=a" and } x = b$

$\text{then the factors of the polynomial are }$

$\left(x - a\right) \text{ and } \left(x - b\right)$

$\text{and the polynomial is the product of the factors}$

$\Rightarrow p \left(x\right) = k \left(x - a\right) \left(x - b\right) \leftarrow \textcolor{b l u e}{\text{k is a multiplier}}$

$\text{here "a=-4" and } b = 5$

$\Rightarrow \left(x + 4\right) \text{ and "(x-5)" are the factors}$

$\Rightarrow p \left(x\right) = k \left(x + 4\right) \left(x - 5\right)$

$\text{let } k = 1$

$\Rightarrow p \left(x\right) = {x}^{2} - x - 20 \text{ is a possible polynomial}$