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