One of the roots of quadratic equation $2 x^{2} + k x - 2 = 0$ is $- 2$ then find $k$ .Also find the other root.

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Solution

Given: One of the root of the equation is $- 2$
Put $x = - 2$ in $2 x^{2} + k x - 2 = 0$
$\Rightarrow 2 {(- 2)}^{2} - 2 k - 2 = 0$
$\Rightarrow 8 - 2 k - 2 = 0$
$\Rightarrow - 2 k = - 6$ or $k = \frac{6}{2} = 3$
The above equation becomes $2 x^{2} + 3 x - 2 = 0$
$2 x^{2} + 4 x - x - 2 = 0$
$\Rightarrow 2 x (x + 2) - 1 (x + 2) = 0$
$∴ (x + 2) (2 x - 1) = 0$
Thus, the other root of the equation is $x = \frac{1}{2}$

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