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Rajan@2021
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Find the zeroes of the quadratic polynomials and verify the relationship between the zeroes and the coefficients: x²-2x-8

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One of the most important and conceptual question from polynomials in which we have given a equation x²-2x-8 and we have to find the zeroes of the polynomial equation and also show the relationship between zeroes and coefficient.

Kindly solve the above equation

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

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1 Answer

  1. f(x)=2x8
    f(x)=4x+2x8
    f(x)=x(x4)+2(x4)]
    f(x)=(x4)(x+2)
    Zeros of f(x) are given by f(x) = 0
    x22x8=0
    (x4)(x+2)=0
    x=4 or x=2
    So, α=4 and β=2
     sum of zeros =α+β=42=2
    Also, sum of zeros =Coefficient of x/Coefficient of x²
    =-(−2)/1=2
    So, sum of zeros =α+β=Coefficient ofx/Coefficient of x²
    Now, product of zeros =αβ=(4)(2)=8
    Also, product of zeros =Constant term/coefficient of x²
    =−8​/1=8
     Product of zeros =Coefficient of x2Constant term=αβ

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