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 BYJU'S Exam Prep
Updated on: October 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
Table of content
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.
Answer:
For Quadratic Polynomial p(x) = 4x2 − 5x − 1, the value of α2β + αβ2 is -5/16
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