If $k > 0$ and the product of the roots of the equation $x^{2} - 3 k x + 2 e^{2 log k} - 1 = 0$ is $7$ then the sum of the roots is:

2

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4

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6

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8

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Solution

The correct option is C $6$
Since the product of roots is $7$
$\frac{c}{a} = 7$
By simplifying and taking natural $log$ $(log$ to the base $e)$ on both sides
$log k^{2} = log 4$
Therefore
$k^{2} = 4$
$k = \pm 2$
Since input value of $log$ cannot be negative
$k = 2$
Therefore sum of the roots
$α + β = - (- 3 k) = 3 (2) = 6$

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