Question

Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2–8x+2

Answer 1

We have to calculate the zeros of the function with the quadratic formula.

`f(x)=x^2-8x+2`
`\begin{gathered} x=(-(-8))/(2\cdot1)\pm\frac{\sqrt[]{(-8)^2-4\cdot1\cdot2}}{2\cdot1}=(8)/(2)\pm\frac{\sqrt[]{64-8}}{2}=4\pm\frac{\sqrt[]{56}}{2}=4\pm\sqrt[]{(56)/(4)}=4\pm\sqrt[]{14} \\ \\ x_1=4+\sqrt[]{14}\approx4+3.742=7.742 \\ x_2=4-\sqrt[]{14}\approx4-3.742=0.258 \end{gathered}`

The roots are x1=7.742 and x2=0.258, both reals., both