Question

10. If a and B are zeroes of a quadratic polynomial P(x) = 4x2-5x-1. Find the value of a²?B+aß²
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Answer 1

Answer:

α and β are zero of the polynomial:

p(x)=4x2-5x-1

a=4,b=-5,c=-1

So, Sum of the zeroes = α + β=-\(\frac ba\) \(= \frac{5}{4}\)

Product of the zeroes = αβ=\(\frac ca\) \(= \frac{{ - 1}}{4}\)

Now, α2β + αβ2 = αβ(α + β)

\(= \frac{5}{4}\left( {\frac{{ - 1}}{4}} \right)\)

\(= \frac{{ - 5}}{{16}}\).