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Rajan@2021
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Find the quadratic polynominal whose zeroes are 2/3 and −1/4 . verify the relation between the coefficients and the zeroes of the polynomial.

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This is the basic and exam oriented question from polynomials in which we have to find the quadratic polynomial and also asked to verify the relationship between the zeroes and coefficient if their zeroes are 2/3 and -1/4.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 2A, question no 14

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1 Answer

  1. Let α=2/3 and β=-1/4

    Sum of the zeroes = (α+β)=2/3+(−1)​/4=5/12

    Product of the zeroes , αβ=2/3×−1/4=−1/6

    Required quadratic polynomial is

    (α+β)x+αβ
    =(5/12)x(−1/6)

    =1/12(125x2)

    and
    sum of the zeroes =5/12=(coefficient of x2)(coefficient of x)

    product of zeroes =6−1=coefficient of x2constant term

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