Answer:
Our problem is [tex]x^2-2x+6=0[/tex], but as we can see, we are unable to factor. We have to use the quadratic equation to solve.
[tex]x^2-2x+6=0[/tex]
[tex]\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
Positive Quadratic Formula:
[tex]\frac{-(-2)+\sqrt{(-2)^2-4(1)(6)}}{2(1)}[/tex]
[tex]=\frac{2+\sqrt{4-24}}{2}\\=1+\frac{\sqrt{-20}}{2}[/tex]
Negative Quadratic Formula:
[tex]\frac{-(-2)-\sqrt{(-2)^2-4(1)(6)}}{2(1)}[/tex]
[tex]=\frac{2-\sqrt{4-24}}{2}\\=1-\frac{\sqrt{-20}}{2}[/tex]
Since both of our answers are the square root of a negative number, we know that the quadratic equation has no real solution.
*We could have also used the Discriminant Test to determine whether the quadratic equation has real roots or not. However, for our means, the quadratic equation seems enough.
