Question

How do you find a polynomial with roots 4, −5, and 7?

Answer 1

`f(x) = x^3-6x^2-27x+140`

Explanation:

Each zero `a` corresponds to a linear factor `(x-a)`, so a suitable polynomial would be:

`f(x) = (x-4)(x+5)(x-7) = x^3-6x^2-27x+140`

Any polynomial in `x` with these zeros will be a multiple (scalar or polynomial) of this `f(x)`.