[tex]5z^{2}+8z+5=0[/tex]
Înainte de toate, formula:
[tex]\boxed{\delta=b^{2}-4ac\\;~~~~\\z_{1,2}=\frac{-b \pm \sqrt{\delta}}{2a}}[/tex]
Deci,
[tex]a=+5\\ \\b=+8\\ \\c=+5\\
\\ \delta=b^{2}-4ac\\
\\ \delta=8^{2}-4 \cdot 5 \cdot 5\\
\\ \delta=64-100=-36[/tex]
Hmm... Delta e negativ, facem atunci cu numere complexe.
Formula:
[tex]\boxed{\delta=b^{2}-4ac\\;~~~~\\z_{1,2}=\frac{-b \pm i\sqrt{-\delta}}{2a}}[/tex]
Si atunci:
[tex]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}}\\
[/tex]
[tex]S=[/tex]{[tex]\frac{-4+3i}{10};~\frac{-4-3i}{10}[/tex]}
