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If α And β Are the Zeros of the Quadratic Polynomial F(X) = Ax2 + Bx + C, Then Evaluate - CBSE Class 10 - Mathematics

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Question

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`

Solution

f(x) = ax2 + bx + c

α + β = `(-b/a)`

αβ = `c/a`

since α + β are the roots (or) zeroes of the given polynomials

then

`beta/(aalpha+b)+alpha/(abeta+b)`

`=(beta(abeta+b)+alpha(aalpha+b))/((aalpha+b)(abeta+b))`

`=(abeta^2+b beta+aalpha^2+balpha)/(a^2alphabeta+abalpha+ab beta+b^2)`

`=(aalpha^2+abeta^2+b beta+balpha)/(a^2xxc/a+ab(alpha+beta)+b^2)`

`=(a(alpha^2+beta^2)+b(alpha+beta))/(ac+ab(-b/a)+b^2)`

`=(a[(alpha+beta)^2-2alphabeta]+bxx-b/a)/(ac-b^2+b^2)`

`=(a[(-b/a)^2-2(c/a)]-b^2/a)/(ac)`

`=((b^2)/a-(2c)-b^2/a)/(ac)`

`=(-2c)/(ac)`

`=(-2)/a`

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 2: Polynomials
Ex. 2.10 | Q: 2.7 | Page no. 35
Solution If α And β Are the Zeros of the Quadratic Polynomial F(X) = Ax2 + Bx + C, Then Evaluate Concept: Relationship Between Zeroes and Coefficients of a Polynomial.
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