Question

What are the roots of the equation5X^2+ x = -1 in simplest a + bi form?

Answer 1

For the equation given below;

$5x^2+x=-1$

We shall move all the expresions to the left side and thus we would have;

$\begin{gathered} 5x^2+x=-1 \\ \text{Add 1 to both sides;} \\ 5x^2+x+1=0 \end{gathered}$

We would now solve for x in the quadratic equation using the quadratic equation formula;

$\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Where;} \\ a=5,b=1,c=1 \\ x=\frac{-1\pm\sqrt[]{1^2-4(5)(1)}}{2(5)} \\ x=\frac{-1\pm\sqrt[]{1-20}}{10} \\ x=\frac{-1\pm\sqrt[]{-19}}{10} \\ x=\frac{-1\pm\sqrt[]{19}i}{10} \\ \text{Therefore, we would now have;} \\ x=\frac{-1+\sqrt[]{19}i}{10},x=\frac{-1-\sqrt[]{19}i}{10} \end{gathered}$

ANSWER:

The roots of the equation are as shown below;

$\begin{gathered} x=\frac{-1+\sqrt[]{19}i}{10} \\ x=\frac{-1-\sqrt[]{19}i}{10} \end{gathered}$