# If $alpha, beta$ are the zeroes of $f( x)=px^2-2x+3p$ and $alpha +beta=alphabeta$, then find the value of $p$.

Given: $\alpha , \ \beta$  are zeroes of the polynomial $f( x)=px^2−2x+3p$, and $\alpha+\beta =\alpha \beta$

To do: To find the value of $p$.

Solution: From the given quadratic equation,

$\alpha +\beta=\frac{2}{p}$ and $\alpha \beta =3$

but it is given,

$\alpha +\beta =\alpha \beta$

$\Rightarrow \frac{2}{p}=3$

$\Rightarrow p=\frac{2}{3}$
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