why is this formula used here?
What will be the answer of α2β+αβ2 when the quadratic polynomial used is p(x) = 4×2 – 5x – 1.
Class 10th mathematics chapter 2nd.
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If α and β are the zeros of the quadratic polynomial p(x) = 4×2 – 5x – 1, find the value of α2β+αβ2.
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Solution:
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
So, we can find
Sum of the roots = α+β = -b/a = – (-5)/4 = 5/4
Product of the roots = αβ = c/a = -1/4
To find, α2β+αβ2
⇒ αβ(α +β)
⇒ (-1/4)(5/4) = -5/16