This question is taken from polynomials in which we have given that x³+2x²-11x-12 is a polynomial and -1 is one of the it’s zeroes and we have to find all the other zeroes.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 2B, question no 12

## Let f(x)=x³+2x²−11x−12

Given : −1 is a zero of the polynomial , which means (x+1) is a factor of f(x)

Dividing f(x) by (x+1) we get

f(x) becomes:

f(x)=(x+1)(x²+x−12)

=(x+1)(x²+4x−3x−12)

=(x+1)(x−3)(x−4)

if f(x)=0

⇒(x+1)(x−3)(x+4)=0

either (x+1)=0 or (x−3)=0 or (x+4)=0

x=−1 or x=3 or x=−4

zeros of the polynomial are −1, 3 and −4