Question

Find the value ofk so.that the sum of the roots of equation
$3 {x}^{2} + {2k + 1}x - k - 5 = 0$
$is \: equal \: to \: the \: product \: of \: the \: roots$

Answer 1

$3 {x}^{2} + (2k + 1)x - (k + 5) = 0 \\ in \: a {x}^{2} + bx + c = 0 \\ sum \: of \: roots = \frac{ - b}{a} \\ product \: of \: roots = \frac{c}{a} \\ here \: sum \: of \: roots = \frac{ - (2k + 1)}{3} \\ product \: of \: roots = \frac{ - (k + 5)}{3} \\ given \: that \: sum = product \\ = > \frac{ - (2k + 1}{3} = \frac{ - (k + 5)}{3} \\ = > 2k + 1 = k + 5 \\ = > k = 4$
hope it helps