Question

Solve $\sqrt{5}{x}^2+x+\sqrt{5}=0$.

Answer 1

Given that quadetric equation is $\sqrt{5}{x}^2+x+\sqrt{5}=0$

[If given qudratics equation as $a{x}^2+bx+c=0$, then $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$]

Then we compare given quadratic equation with standrad form, we get $a=\sqrt{5},b=1,c=\sqrt{5}$, then

$x=\frac{-1\pm \sqrt{1-(4\times \sqrt{5}\times \sqrt{5})}}{2\sqrt{5}}$

$x=\frac{-1\pm \sqrt{-19}}{2\sqrt{5}}$

$x=\frac{-1+\sqrt{19}i}{2\sqrt{5}}$and $x=\frac{-1-\sqrt{19}i}{2\sqrt{5}}$