Question

Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2–4x+6

Answer 1

We have to calculate the zeros of the function:

`f(x)=x^2-4x+6`

We apply the quadratic formula:

`\begin{gathered} x=(-(-4))/(2\cdot1)\pm\frac{\sqrt[]{(-4)^2-4\cdot1\cdot6}}{2\cdot1} \\ x=(4)/(2)\pm\frac{\sqrt[]{16-24}}{2} \\ x=2\pm\sqrt[]{(-8)/(4)} \\ x=2\pm\sqrt[]{-2} \\ x=2\pm\sqrt[]{2\cdot(-1)} \\ x=2\pm\sqrt[]{2}\cdot i \\ x\approx2\pm1.414\cdot i \end{gathered}`

The roots are imaginary, and have a value of x1=2+1.414i and x2=2-1.414i.