factoring complex numbers

Question

0

695

1

Factor x^2 + 7x + 19 over the set of complex numbers.

Guest May 19, 2014

+118724

+3

Best Answer

x² + 7x + 19

$$If \qquad x^2+7x+19=0 \mbox{ which it doesn't - then}\\\\
x=\frac{-7\pm \sqrt{49-76}}{2}\\\\
x=\frac{-7\pm(\sqrt{17})i}{2}\\\\$$

SO

$$x^2+7x+19=\left(x+\frac{7+(\sqrt{17})i}{2}\right)
\left(x+\frac{7-(\sqrt{17})i}{2}\right)$$

I think that is ok.

Melody May 20, 2014

Melody · Answer 1 · 2014-05-20T10:45:33

x² + 7x + 19

$$If \qquad x^2+7x+19=0 \mbox{ which it doesn't - then}\\\\
x=\frac{-7\pm \sqrt{49-76}}{2}\\\\
x=\frac{-7\pm(\sqrt{17})i}{2}\\\\$$

SO

$$x^2+7x+19=\left(x+\frac{7+(\sqrt{17})i}{2}\right)
\left(x+\frac{7-(\sqrt{17})i}{2}\right)$$

I think that is ok.