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Absolute Value Function

x2 - 10ax - 1...

Question

$x^{2} - 10 a x - 11 b = 0 r o o t s = c, d$
$x^{2} - 10 c x - 11 d = 0 r o o t s = a, b$ find a + b + c + d.

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Solution

$x^{2} - 10 a x - 11 b = 0$ roots $= c, d$
$x^{2} - 10 c x - 11 d = 0$ roots $= a, b$
$c + d = - (- 10 a) = 10 a$
and $a + b = - (- 10 c) = 10 c$
$a + b + c + d = 10 a + 10 c = 10 (a + c)$

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