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If 𝛼 and 𝛽 Are the Zeros of the Quadratic Polynomial F(X) = X2 − 3x − 2, Find a Quadratic Polynomial Whose Zeroes Are `1/(2alpha+Beta)+1/(2beta+Alpha)` - Mathematics

If α and β are the zeros of the quadratic polynomial f(x) = x2 − 3x − 2, find a quadratic polynomial whose zeroes are `1/(2alpha+beta)+1/(2beta+alpha)`

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Since α and β are the zeros of the quadratic polynomial f(x) = x2 − 3x − 2

The roots are α and β

`alpha+beta="-coefficient of x"/("coefficient of "x^2)`


α + β = -(-3)

α + β = 3

`alphabeta="constant term"/("coefficient of "x^2)`


αβ = -2

Let S and P denote respectively the sum and the product of zero of the required polynomial . Then,


Taking least common factor then we have ,







By substituting α + β = 3 and αβ = -2 we get,











By substituting α + β = 3 and αβ = -2 we get,






Hence ,the required polynomial f(x) is given by

`f(x) = k(x^2 - Sx + P)`

`f(x) = k(x^2-9/16x+1/16)`

Hence, the required equation is `f(x) = k(x^2-9/16x+1/16)` Where k is any non zero real number.

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RD Sharma Class 10 Maths
Chapter 2 Polynomials
Exercise 2.1 | Q 16 | Page 35
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