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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 as 5, -2 and -24 respectively.

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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

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  1. This answer was edited.

    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.

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