Find the value(s) of $k$ for which the equation $x^{2} - 2 x + k = 0$ has equal roots.

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Solution

$x^{2} - 2 x + k = 0$
A Quadratic equation has equal roots only if $b^{2} = 4 a c$
$2^{2} = 4 k 4 k = 4 k = 1$

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