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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 α2β + αβ2.
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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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