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Determinant

If α,β are ...

Question

If $α, β$ are the roots of $x^{2} - 2 x + 4 = 0,$ then $\frac{α}{β}$ is equal to $\frac{1}{2} (- 1 \pm \sqrt{3 i})$

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Solution

$α + β = 2, α β = 4 ∴ \frac{(α + β)^{2}}{α β} = \frac{4}{4} = 1$
$\frac{α}{β} + \frac{β}{α} + 2 = 1 o r t + \frac{1}{t} + 1 = 0 w h e r e t = \frac{α}{β}$
$o r t^{2} + t + 1 = 0 ∴ t = ω, ω^{2}$
$o r \frac{- 1 \pm i \sqrt{3}}{2}$

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