Question

Solve the following quadratic equations.

$x^2-5ix-6=0$

Answer 1

Here $a=1,b=-5i$ (complex number) and $c=-6$

$\alpha =\frac{-b+\sqrt{b^2-4ac}}{2a}$ and $\beta =\frac{-b-\sqrt{b^2-4ac}}{2a}$

$\alpha =\frac{(-(-5i)+\sqrt{(-5i{)}^2-4\times 1\times (-6\left)\right)}}{2\times 1}$

$=(5i+i)/2$

$=3i$

$\beta =\frac{-(-5i)-\sqrt{(-5i{)}^2-4\times 1\times (-6)}}{2\times 1}$

$=(5i-i)/2$

$=2i$

So, the roots of the given equation are $3i$ and $2i$.