If α and β are the Zeros of the Quadratic Polynomial p(x) = 4x2 − 5x − 1, Find the Value of α2β + αβ2.
To find the value of α2β + αβ2, we need to substitute the zeros of the quadratic polynomial p(x) = 4x2 - 5x - 1 into the expression.
From Vieta's formulas
We have the sum of the zeros is equal to -b/a
α + β = 5/4 and
the product of the zeros is equal to c/a
αβ = -1/4
Now, we can calculate α2β + αβ2:
α2β + αβ2 = αβ(α + β) + αβ(α + β)
Substituting the values we know:
= (-1/4)(5/4) = -5/16
Therefore, the value of α2β + αβ2 is -5/16.
For Quadratic Polynomial p(x) = 4x2 − 5x − 1, the value of α2β + αβ2 is -5/16
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