#### Question

If 𝛼 and 𝛽 are the zeros of the quadratic polynomial p(x) = 4x^{2} − 5x −1, find the value of α^{2β} + αβ^{2}.

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#### Solution

Since 𝛼 𝑎𝑛𝑑 𝛽 are the roots of the polynomial: 4𝑥^{2} − 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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#### Reference Material

Solution for question: 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. For the course CBSE