This is the basic and conceptual question from polynomials in which we have given the zeroes 5, -2, -24 and we have to find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 2B, question no 5
As we know , general form of cubic polynomial whose zeroes are a, b and c is :
x³−(a+b+c)x²+(ab+bc+ca)x−abc
also written as :
x³−(sum of zeroes)x²+(sum of the product of zeroes taking two at a time)x−(product of zeroes)………….(1)
Given :
Sum of zeros =5
Sum of the product of its zeros taken two at a time=−2
Product of its zeros =−24
Putting these values in equation (1) we get:
x³−5x²−2x+24
which is required polynomial.