Question

How do you find all the zeros of `f(x)=x^3+5x^2-4x-20`?

Answer 1

x = -5 , x = ± 2

Explanation:

The zeros of f(x) are the values of x that make f(x) = 0

solve: `x^3+5x^2-4x-20=0`

Begin by factorising the left side. Group the term in 'pairs'

`[x^3+5x^2]+[-4x-20]` and factorising each pair gives.

`x^2(x+5)-4(x+5)=(x+5)(x^2-4)`

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

Solving `(x+5)(x-2)(x+2)=0`

The zeros are `x=-5,x=±2`