Answer: No solutions
Step-by-step explanation:
There are no solutions to 0 = x² - x + 1.
[Method One]
We can solve this by rewriting the equation, but it is quicker to graph it when there are no solutions. See attached.
[Method Two]
I said we can solve this by solving an equation, here it is. We will use the quadratic formula since the equation given is already in the proper form.
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\displaystyle x=\frac{1\pm\sqrt{(-1)^2-4(1)(1)} }{2(1)}[/tex]
[tex]\displaystyle x=\frac{1\pm\sqrt{-3} }{2}[/tex]
-> Negative numbers don't have real square roots, so there is no solution
