Question

$5 {z}^{2} +8z +5 =0$

Answer 1

$5z^{2}+8z+5=0$

Înainte de toate, formula:

$\boxed{\delta=b^{2}-4ac\\;~~~~\\z_{1,2}=\frac{-b \pm \sqrt{\delta}}{2a}}$


Deci,

$a=+5\\ \\b=+8\\ \\c=+5\\ \\ \delta=b^{2}-4ac\\ \\ \delta=8^{2}-4 \cdot 5 \cdot 5\\ \\ \delta=64-100=-36$

Hmm... Delta e negativ, facem atunci cu numere complexe.
Formula:


$\boxed{\delta=b^{2}-4ac\\;~~~~\\z_{1,2}=\frac{-b \pm i\sqrt{-\delta}}{2a}}$

Si atunci:

$z_{1,2}=\frac{-8 \pm i\sqrt{-(-36)}}{2 \cdot 5}\\ \\ z_{1,2}=\frac{-8 \pm i\sqrt{36}}{10}=\\ \\ z_{1,2}=\frac{-8 \pm 6i}{10}=\frac{2(-4 \pm 3i)}{10}=\frac{-4 \pm 3i}{10}\\ \\ \boxed{z_{1}=\frac{-4+3i}{10}}\\ \\ \boxed{z_{2}=\frac{-4-3i}{10}}$

$S=${$\frac{-4+3i}{10};~\frac{-4-3i}{10}$}