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

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) 

⇒ (\(\frac{-1}{4}\))(\(\frac{5}{4}\)) 

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