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Solving Using Quadratic Formula When D>0

For what valu...

Question

For what values of k, x=a is a solution of the equation $x^{2} - (a + b) x + k = 0$ .

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Solution

$x^{2} - (a + b) x + k = 0$
Put $x = a$
$a^{2} - (a + b) a + k$
$a^{2} - a^{2} + a b + k = 0$
$a b + k = 0$
$k = - a b$

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