If $m$ and $n$ are zeros of the polynomial $a x^{2} - 5 x + c$ , find the value of $c$ if $m + n = m n$ .

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Solution

$\begin{matrix} m + n = \frac{5}{a} m . n = \frac{c}{a} \frac{5}{a} = \frac{c}{a} c = 5. \end{matrix}$

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