Question

How do you find a polynomial function that has zeros 0, 2, 5?

Answer 1

`f(x)=x^3-7x^2+10x`

Explanation:

Let `f(x)` be the required polynomial.

We are told that `f(x)=0` for `x={0, 2, 5}`

Thus: `x, (x-2), (x-5)` must be factors of `f(x)`

`:. f(x) = x(x-2)(x-5)`

`= x(x^2-7x+10)`

`=x^3-7x^2+10x`