# If α and β are the Zeros of the Quadratic Polynomial p(x) = 4x^2 − 5x − 1, Find the Value of α^2β + αβ^2

By Mohit Uniyal|Updated : May 17th, 2023

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

Given the quadratic polynomial p(x) = 4x2 - 5x - 1, we assume that α and β are the zeros of this polynomial.

Apply formulas:

• The sum of the zeros α + β is equal to -(-5)/4 = 5/4.
• The product of the zeros αβ is equal to -1/4.

We are asked to find the value of α2β + αβ2. To do this, we substitute the values of α + β and αβ into the expression: α2β + αβ2 = αβ(α + β)

Replace α + β with 5/4 and αβ with -1/4 in the expression: α2β + αβ2 = (-1/4)(5/4)

Simplify the expression

## If α and β are the Zeros of the Quadratic Polynomial p(x) = 4x2 − 5x − 1, Find the Value of α2β + αβ2.

Solution:

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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