Question

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

Answer 1

Begin with the factored form to find that one such polynomial is

`P(x) = x^3 +2x^2 - 13x + 10`

Explanation:

A simple way of generating a polynomial with given roots is to begin with it in factored form. If `(x-x_0)` is a factor of a polynomial `P(x)`, then `P(x_0) = 0` and so `x_0` is a root of `P(x)`.

Applying this here, we get

`P(x) = (x-(-5))(x-1)(x-2)`

Again, plugging in any of the desired roots immediately yields `0`, meaning the polynomial has the desired properties. Then, all that remains is to multiply it out.

`P(x) = (x+5)(x-1)(x-2)`

`= x^3 + 2x^2 -13x + 10`