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

1 Answer
Jul 18, 2016

Answer:

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#