Question

If $\alpha and \beta$ are the zeros of the quadratic polynomial $p(x) = 4x^{2} -5x-1$,find the value of $\alpha^{2} \beta + \alpha \beta^{2}$

Answer 1

SOLUTION :

Given :  α and β are the zeroes of the quadratic polynomial p(x)= 4x² - 5x - 1

On comparing with ax² + bx + c,

a = 4 , b= -5 , c= -1

Sum of the zeroes = −coefficient of x / coefficient of x²

α + β  = -b/a = -(-5)/4 = 5/4

α + β = 5/4 ………………………..(1)

Product of the zeroes = constant term/ Coefficient of x²

αβ = c/a = -¼

αβ =  −1/4 ………………..(2)

Now,

α²β+αβ² = αβ(α+β)

By Substituting the value from eq 1 & 2

= 5/4(−1/4)

= −5/16

Hence, the value of α²β+αβ² is -5/16.

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