Question

Solve the quadratic equation x2 − 6x + 13 = 0 using the quadratic formula. What is the solution when expressed in the form a ± bi, where a and b are real numbers?

Answer 1

The given quadratic equation is:

`x^2-6x+13=0`

The quadratic formula is given by the equation:

`x=\frac{-b\pm\sqrt[]{b^2-4ac^{}}}{2a}`

From the given quadratic equation;

`a=1;b=-6\text{ and c=13}`

Thus, we have:

`x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(1)(13)}}{2(1)}`

`\begin{gathered} x=\frac{6\pm\sqrt[]{36-52}}{2} \\ x=\frac{6\pm\sqrt[]{-16}}{2} \\ In\text{ complex form, the }\sqrt[]{-16}=4i \\ \text{Thus, we have:} \\ x=(6\pm4i)/(2) \\ x=(6)/(2)\pm(4i)/(2) \\ x=3\pm2i \end{gathered}`

Hence, the correct option is Option A