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

This answer was edited.## As we know , general form of cubic polynomial whose zeroes are a, b and c is :

xÂ³âˆ’(a+b+c)xÂ²+(ab+bc+ca)xâˆ’abc

also written as :

xÂ³âˆ’(sumÂ ofÂ zeroes)xÂ²+(sumÂ ofÂ theÂ productÂ ofÂ zeroesÂ takingÂ twoÂ atÂ aÂ time)xâˆ’(productÂ ofÂ zeroes)………….(1)

Given :

Sum of zerosÂ =5

Sum of the product of its zeros taken two at a time=âˆ’2

Product of its zerosÂ =âˆ’24

Putting these values in equation (1) we get:

xÂ³âˆ’5xÂ²âˆ’2x+24

which is required polynomial.