Question

if -2 is a zero of f(x)=x^3+13x^2+32+20 , find its other zeroes​

Answer 1

Given,

f(x) = x^3 + 13x^2 + 32x +20

if, -2 is a zero then (x+2) is a solution of it. Let, f(x)=0

So,

x^3 + 13x^2 + 32x +20 = 0

or, x^3 + 2x^2 + 11x^2 +22x + 10x + 20 = 0

or, x^2(x+2) +11x(x+2) + 10(x+2) = 0

or, (x+2) ( x^2+11x+10) = 0

Then,

x = -2

and,

x^2+11x+10 = 0

or, x^2 +10x+x+10 = 0

or, x(x+10) + 1(x+10) = 0

or, (x+10) (x+1) = 0

so,

x = -10 and x = -1

Answer: x=-2, -10,-1