Question

if alpha and beta are the zeros of the polynomial 4x-5x-1, find the value of alpha2beta+ alphabeta2​

Answer 1

Answer:

α²β + αβ² = -5/16

Step-by-step explanation:

Given quadratic polynomial is 4x²-5x-1. Also, α and β are its zeros.

⇒ α+β = -b/a = -(-5)/4 = 5/4      (Sum of zeros)

And, αβ = c/a = -1/4      (Product of zeros)

So, α²β+αβ² = (αβ)(α+β)

⇒ α²β+αβ² = (-1/4)(5/4)

or α²β+αβ² = -5/16

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