First slide

Theory of equations

Question

The polynomial equation of the lowest degree having roots 1, $\sqrt{3} i$ is

Easy

A

$x^{3} + x^{2} + 3 x + 3 = 0$
B

$x^{3} - x^{2} + 3 x - 3 = 0$
C

$x^{3} + x^{2} - 3 x - 3 = 0$
D

$x^{3} - x^{2} - 3 x + 3 = 0$

Solution

Roots $α = 1, β = \sqrt{3} i, γ = - \sqrt{3} i$
$(x^{2} + 3) (x - 1) = 0$
$\Rightarrow x^{3} - x^{2} + 3 x - 3 = 0$

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