Q. 124.6( 16 Votes )

# If α and β are the zeros of the quadratic polynomial p(x) = 4x^{2} – 5x – 1, find the value of α^{2}β + αβ^{2}

Answer :

**Concept Used:**

For a quadratic polynomial,

P(x) = ax^{2} + bx + c

Sum of the roots

The product of roots

**Given:**

p(x) = 4x^{2} – 5x – 1

**Explanation:**

For given p(x), we get

a = 4, b = –5, and c = –1

α^{2}β + αβ^{2} = αβ(α + β)

α^{2}β + αβ^{2}

**Hence, the value of** **α ^{2}β + αβ^{2} is –5/16.**

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