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If 𝛼 and 𝛽 Are the Zeros of the Quadratic Polynomial P(X) = 4x2 − 5x −1, Find the Value of α2β + αβ2. - CBSE Class 10 - Mathematics

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Question

If 𝛼 and 𝛽 are the zeros of the quadratic polynomial p(x) = 4x2 − 5x −1, find the value of α + αβ2.

Solution

Since 𝛼 𝑎𝑛𝑑 𝛽 are the roots of the polynomial: 4𝑥2 − 5𝑥 − 1

∴ Sum of the roots `alpha+beta=5/4`

Product of the roots `alphabeta=(-1)/4`

Hence `alpha^2beta+alphabeta^2=alphabeta(alpha+beta)=5/4((-1)/4)=(-5)/16`

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APPEARS IN

 RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 2: Polynomials
Ex.2.10 | Q: 5 | Page no. 34
Solution If 𝛼 and 𝛽 Are the Zeros of the Quadratic Polynomial P(X) = 4x2 − 5x −1, Find the Value of α2β + αβ2. Concept: Relationship Between Zeroes and Coefficients of a Polynomial.
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