Question

Resolva a equação x2-6x+10=0, no conjunto dos números complexos. ALTERNATIVAS
S={3-i, 3-i}
S={3+i, 6-i}
S={3+i, 3-i}
S={3+i, 3+i}
S={3-i, 6-i}

Answer 1

$x^{2}-6x+10=0$

$\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

$\Rightarrow \frac{-(-6)\pm \sqrt{(-6)^{2}-4\cdot 1\cdot 10}}{2\cdot1}$

$\Rightarrow \frac{6\pm \sqrt{36-40}}{2}$

$\Rightarrow \frac{6\pm \sqrt{-4}}{2}$

$\Rightarrow \frac{6\pm 2\cdot\sqrt{-1}}{2}$

$\Rightarrow \frac{6\pm 2\cdot i}{2}$

$\Rightarrow 3\pm i$

$S={3+i,3-i}$