Question

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

Answer 1

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(x) = (x-1) * (x-(-2)) * (x-5) =`
`=x^3 - 4*x^2 - 7*x + 10`

If you ever want to find a polynomial that has `x_1`,`x_2`,...,`x_n` as roots:
`p(x) = (x-x_1) * (x-x_2) * ... * (x-x_n)`

Hope it helps