Question

What are the roots of the equation 9x2 + 30x + 29 = 0 in simplest a + bi form?

Answer 1

Determine the roots of the equation by using the quadratic formula.

`\begin{gathered} x=\frac{-30\pm\sqrt[]{(30)^2-4\cdot9\cdot29}}{2\cdot9} \\ =\frac{-30\pm\sqrt[]{900-1044}}{18} \\ =\frac{-30\pm\sqrt[]{-144}}{18} \\ =(-30\pm12i)/(18) \\ =-(30)/(18)\pm(12i)/(18) \\ =-(5)/(3)\pm(2)/(3)i \end{gathered}`

Thus roots of the equation are,

`-(5)/(3)+(2)/(3)i`

and

`-(5)/(3)-(2)/(3)i`