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Algebra of Complex Numbers

If α ,β are...

Question

If $α, β$ are the roots of the equation $x^{2} - 2 x - 3 = 0$ , then find $α - 2 β$

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Solution

$x^{2} - 2 x - 3 = 0 x^{2} - 3 x + x - 3 = 0 x (x - 3) + 1 (x - 3) = 0 (x + 1) (x - 3) = 0 x = - 1, 3$
$α = - 1, β = 3 α - 2 β - 1 - 2 (3) = - 1 - 6 = - 7$

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