Question

Encontre as raízes complexas da equação a seguir x^2 + 2x + 5 = 0.

Answer 1

Explicação passo-a-passo:

$x^2+2x+5=0$

$\Delta=2^2-4\cdot1\cdot5$

$\Delta=4-20$

$\Delta=-16$

$\Delta=16\cdot(-1)$

$\Delta=16i^2$

$x=\dfrac{-2\pm\sqrt{16i^2}}{2\cdot1}=\dfrac{-2\pm4i}{2}$

$x'=\dfrac{-2+4i}{2}~\longrightarrow~x'=-1+2i$

$x"=\dfrac{-2-4i}{2}~\longrightarrow~x"=-1-2i$

$S=\{-1-2i,-1+2i\}$