Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$x^{2} - 6 x + 4 = 0$

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Solution

$x^{2} - 6 x + 4 = 0$

$d^{2} = b^{2} - 4 a c$
$= 36 - 16 = 20$
$d = \pm 2 \sqrt 5$

$x = - b / 2 a \pm d / 2 a$
$= 6 / 2 \pm 2 \sqrt 5 / 2 = 3 \pm \sqrt 5$

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