Sir please give me a detailed solution of this question which is taken from polynomials chapter in which we have given a polynomial (x³-4x²-7x+10) and 1 and -2 are two zeroes of the given polynomial and we have been asked to find its third zero.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 2B, question no 13
Let f(x)=x³−4x²−7x+10
Given : 1 and −2 are the zeros of the given polynomial therefore (x−1) and (x+2) are factors of f(x)
Consequently ,(x−1)(x+2)=(x²+x−2) is a factor of f(x)
Divide x³−4x²−7x+10 by (x²+x−2)
put f(x)=0
(x²+x−2)(x−5)=0
(x−1)(x+2)(x−5)=0
x=1 or x=−2 or x=5
hence , the third zero is 5.