Question

Write a polynomial equation with integer coefficients that has the given roots

x=0
x=-5
x=4
​

Answer 1

y = x³ +x² -20x

Explanation:

You want a polynomial with roots x ∈ {0, -5, 4}.

Factors

When a polynomial has a root p, it has a factor (x -p). The three given roots mean the polynomial you want can be factored as ...

y = (x -0)(x -(-5))(x -4) = x(x+5)(x-4)

When this product is expanded, the result is ...

y = x³ +x² -20x . . . . polynomial with roots {0, -5, 4}