Question

`11r {}^(2) + 10 = 0`solve the equation with the quadratic formula.

Answer 1

We have the expression:

`11r^2+10=0`

We can write the quadratic equation as:

`\begin{gathered} r=-(0)/(2\cdot11)\pm\frac{\sqrt[]{0^2-4\cdot11\cdot10}}{2\cdot11} \\ r=\pm\frac{\sqrt[]{-440}}{22} \\ r=\pm\frac{\sqrt[]{4\cdot(-110)}}{22} \\ r=\pm(2)/(22)\sqrt[]{-110} \\ r=\pm\frac{\sqrt[]{110}}{11}i \\ r=\pm\sqrt[]{(11\cdot10)/(11\cdot11)i} \\ r=\pm\sqrt[]{(10)/(11)}i \end{gathered}`

The roots of the expression are r=-√(10/11)*i and r=√(10/11)*i (complex roots).