If α and β are the zeros of the quadratic polynomial p(x) = 4x2 –

1.	If α and β are the zeros of the quadratic polynomial p(x) = 4x2 – 5x – 1, find the value of α2β + αβ2.
Answer» From the question, it’s given that: α and β are the roots of the quadratic polynomial p(x) where a = 4, b = -5 and c = -1 Sum of the roots = α+β = \(\frac{-b}{a}\) = – \(\frac{(-5)}{4}\) = \(\frac{5}{4}\) Product of the roots = αβ = \(\frac{c}{a}\) = \(\frac{-1}{4}\) α²β + αβ² ⇒ αβ(α +β) ⇒ (\(\frac{-1}{4}\))(\(\frac{5}{4}\)) = \(\frac{-5}{16}\)

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

Answer»

From the question, it’s given that:

α and β are the roots of the quadratic polynomial p(x) where a = 4, b = -5 and c = -1

Sum of the roots = α+β = \(\frac{-b}{a}\)

= – \(\frac{(-5)}{4}\)

= \(\frac{5}{4}\)

Product of the roots = αβ = \(\frac{c}{a}\)

= \(\frac{-1}{4}\)

α²β + αβ²

⇒ αβ(α +β)

⇒ (\(\frac{-1}{4}\))(\(\frac{5}{4}\))

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