Find the value of $k$ for which $x = 3$ is a solution of the quadratic equation, $(k + 2) x^{2} - k x + 6 = 0$ .
Thus find the other root of the equation.

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Solution

Given : $(k + 2) x^{2} - k x + 6 = 0$
Putting $x = 3$
$(k + 2) \times 9 - k \times 3 + 6 = 0$
$9 k + 18 - 3 k + 6 = 0$
$6 k = - 24$
$k = - 4$
Putting $k = - 4$ in given equation
$- 2 x^{2} + 4 x + 6 = 0$
$x^{2} - 2 x - 3 = 0$
$x^{2} - 3 x + x - 3 = 0$
$x (x - 3) + 1 (x - 3) = 0$
$(x + 1) (x - 3) = 0$
$x + 1 = 0$ or $x - 3 = 0$
$x = - 1$ or $x = 3$
Other root of the equation, $x = - 1$

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