Question

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

Answer 1

α and β are the zeros of the quadratic polynomial p(x) = 4x² - 5x - 1

Sum of the roots = α + β = \(\frac{constant\,term}{coefficient\,of\,x^2}\) = - \(\frac{(-5)}{4}\) = \(\frac{5}{4}\)

Product of the roots = α x β = \(\frac{constant\,term}{coefficient\,of\,x^2}\) = \(\frac{(-1)}{4}\)

Now,

α²β + αβ² =αβ(α + β)

On substituting values from above, we get

= \(\frac{-1}{4}\) × \(\frac{5}{4}\) = - \(\frac{5}{16}\)