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

Video Explanation

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Solution

Given polynomial:

p(x) = 4x² − 5x − 1

Step 1: Find α + β and αβ

Comparing p(x) = 4x² − 5x − 1 with ax² + bx + c:

a = 4,   b = −5,   c = −1

α + β = −b/a = 5/4

αβ = c/a = −1/4

Step 2: Find the Required Value

α²β + αβ²

= αβ(α + β)

= (−1/4)(5/4)

= −5/16

Final Answer

The required value is −5/16.

Conclusion

Thus, using the relationship between zeros and coefficients of the quadratic polynomial, the value of the given expression is correctly obtained.