If $α$ and $β$ are the zeros of the quadratic polynomial $p(x)\ =\ 4x^2\ –\ 5x\ –\ 1$, find the value of $α^2β\ +\ αβ^2$.
 Given:
$α$ and $β$ are the zeros of the quadratic polynomial $p(x) =4x^2-5x- 1$.
To do:
Here, we have to find the value of $α^2β+β^2α$.
Solution:  
We know that,
The standard form of a quadratic polynomial is $ax^2+bx+c$, where a, b and c are constants and $a≠0$.
Comparing the given polynomial with the standard form of a quadratic polynomial,
$a=4$, $b=-5$ and $c=-1$
Sum of the roots $= α+β = \frac{-b}{a} = \frac{–(-5)}{4} = \frac{5}{4}$.
Product of the roots $= αβ = \frac{c}{a} = \frac{-1}{4}$
Therefore,
$α^2β+β^2α=αβ(α+β)$
$=\frac{-1}{4} (\frac{5}{4})$
$=\frac{-1\times5}{4\times4}$
$=\frac{-5}{16}$
The value of $α^2β+β^2α$ is $\frac{-5}{16}$.
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