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Find a cubic polynomial whose zeroes are 1/2,1 and -3.

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This is the basic and conceptual question from polynomials in which we have given zeroes 1/2, 1 and -3 and we have to find the cubic polynomial

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 2B, question no 4

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  1. General Form of cubic polynomial whose zeroes are a. b and c is :
    x³−(a+b+c)x²+(ab+bc+ca)x−abc..........(1)

    To find : cubic polynomial whose zeroes are 1/2​,1 and –3

    Let us say , a=1/2​,b=1 and c=−3
    Putting the values of a,b and c in equation (1) we get :

    =x³−(1/2+1−3)x²+(1/2​−3−3/2​)x−(−3/2​)

    =x³−(−3)/2​x²−4x+3/2

    =2x³+3x²−8x+3
    which is required polynomial.

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