If one root of $x^{2} - 5 x + k = 0$ is 2, then find the value of k and the other root.

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Solution

$2^{2} - 5 (2) + k = 0$
(since 2 is one root)
$4 - 10 + k = 0 k = 6$
equation will be $x^{2} - 5 x + 6 = 0$
$(x - 3) (x - 2) = 0$
$x = 3, 2$
Hence, other root of the equation is 3.

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