# How do you find the polynomial function with roots 1, –2, and 5?

There is more than one polynomial function with roots $1$,$- 2$ and $5$, but if those are the only roots, and none of them is root more than once, the function is:
$p \left(x\right) = \left(x - 1\right) \cdot \left(x - \left(- 2\right)\right) \cdot \left(x - 5\right) =$
$= {x}^{3} - 4 \cdot {x}^{2} - 7 \cdot x + 10$
If you ever want to find a polynomial that has ${x}_{1}$,${x}_{2}$,...,${x}_{n}$ as roots:
$p \left(x\right) = \left(x - {x}_{1}\right) \cdot \left(x - {x}_{2}\right) \cdot \ldots \cdot \left(x - {x}_{n}\right)$