If α and β are the zeros of the quadratic polynomial p(x) = 4x2 – 5x – 1, find the value of α2β + αβ2

Concept Used:

P(x) = ax2 + bx + c

Sum of the roots

The product of roots

Given:

p(x) = 4x2 – 5x – 1

Explanation:

For given p(x), we get

a = 4, b = –5, and c = –1

α2β + αβ2 = αβ(α + β)

α2β + αβ2

Hence, the value of α2β + αβ2 is –5/16.

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