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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

ConceptRelationship Between Zeroes and Coefficients of a Polynomial

#### 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

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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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