If one root of the quadratic equation $2 x^{2} + k x - 6 = 0$ is 2, find the value of k. Also, find the other root.

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Solution

Since x=2 is a root of the equation
$2 x^{2} + k x - 6 = 0$
$2 k + 2 = 0$
$k = - 1$
Putting k =-1 in the given equation, we get,
$2 x^{2} - x - 6 = 0$
$(x - 2) (2 x + 3) = 0$
$x = 2, - \frac{3}{2}$
Hence, the other root is $- \frac{3}{2}$ .

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