Sir please give me a detailed solution of this question as it is taken from polynomials chapter in which we have a polynomial (x^4+x³-11x²-9x+18) and 3 and -3 are two zeroes of the given polynomial and we have to find the all other zeroes.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 2B, question no 14
Given : 3 and -3 are the zeroes of the polynomial (x+3) and (x−3) are factors of f(x), and consequently (x−3)(x+3)=(x²−9) is factor of f(x)
Divide f(x) by (x²−9) we get
Put f(x)=0
(x²+x−2)(x²−9)=0
(x−1)(x+2)(x−3)(x+3)=0
x=1 or x=−2 or x=3 or x=−3
hence all the zeros of the given polynomial are 1, −2, 3 and −3.