Question

Consider the following quadratic equation. Then solve the quadratic equation using the formula. Select the number and type of solutions.

Answer 1

`-x^2+3x-7=0`

From the equation:

`\begin{gathered} a=-1 \\ b=3 \\ c=-7 \end{gathered}`

So:

`\begin{gathered} \Delta=b^2-4ac \\ \Delta=3^2-4(-1)(-7) \\ \Delta=9-28 \\ \Delta=-19 \end{gathered}`

Since:

`\Delta<0`

It has 2 imaginary solutions or 2 non-real solutions. The solutions are given by:

`\begin{gathered} x=\frac{-3\pm\sqrt[]{-19}}{-2} \\ x=(3)/(2)+\frac{\sqrt[]{19}}{2}i \\ and \\ x=(3)/(2)-\frac{\sqrt[]{19}}{2}i \end{gathered}`