If the product of the zeroes of the polynomial $a x^{2} - 5 x + 6$ is $5$ then find the value of $a$ .

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Solution

$\Rightarrow$ Let zeros are $α$ and $β$ of the given polynomial $a x^{2} - 5 x + 6 = 0$
$\Rightarrow$ Here, $A = a, B = - 5, C = 6$
$\Rightarrow$ $α β = 5$ [ Given ]
$\Rightarrow$ $\frac{C}{A} = 5$

$\Rightarrow$ $\frac{6}{a} = 5$

$∴$ $a = \frac{6}{5}$

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