Answer:
The roots of the equation for the given quadratic equation is [tex]-2\pm \frac{\sqrt{6}}{2}[/tex] .
Step-by-step explanation:
Given quadratic equation as :
2 x² + 8 x + 5 = 0
The roots of the quadratic equation ax² + bx + c = 0 as can be find as :
x = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]
x = [tex]\frac{-8\pm \sqrt{8^{2}-4\times 2\times 5}}{2\times 2}[/tex]
or, x = [tex]\frac{-8\pm \sqrt{64-40}}{4}[/tex]
Or, x = [tex]\frac{-8\pm \sqrt{24}}{4}[/tex]
Or, x = [tex]\frac{-8\pm 2\sqrt{6}}{4}[/tex]
∴ x = [tex]-2\pm \frac{\sqrt{6}}{2}[/tex]
Hence The roots of the equation for the given quadratic equation is [tex]-2\pm \frac{\sqrt{6}}{2}[/tex] . Answer
