# How do you find a polynomial function with zeroes 5,-3?

The requested polynomial is ${x}^{2} - 2 x - 15$

#### Explanation:

If it is a polynomial like this

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

Generally if you have roots ${r}_{1} , {r}_{2}$ the polynomial is given by

$\left(x - {r}_{1}\right) \cdot \left(x - {r}_{2}\right)$