Question

How do you find a polynomial function that has zeros 4, -3, 3, 0?

Answer 1

`f(x) = x^4-4x^3-9x^2+36x`

Explanation:

If `f(x)` has zeros of `4, -3, 3, 0 -> (x-4), (x+3), (x-3), x` are factors of `f(x)`

Hence: `f(x) = (x-4)(x+3)(x-3)x`

`f(x) = x(x-4)(x^2-9)`

`= (x^2-4x)(x^2-9)`

`= x^4-4x^3-9x^2+36x`