Question

What are the solutions to 0=x^2-x+1?​

Answer 1

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.

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

$\displaystyle x=\frac{1\pm\sqrt{(-1)^2-4(1)(1)} }{2(1)}$

$\displaystyle x=\frac{1\pm\sqrt{-3} }{2}$

   -> Negative numbers don't have real square roots, so there is no solution