Q12 of 25 Page 2

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

Concept Used:


For a quadratic polynomial,


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 –1/16.


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