Final Answer
$x=\frac{1+\sqrt{-3}}{2},\:x=\frac{1-1\cdot \sqrt{-3}}{2}$
Step-by-step explanation
Problem to solve:
$x^2-x+1=0$
1
To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=1$, $b=-1$ and $c=1$. Then substitute the values of the coefficients of the equation in the quadratic formula:
- $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$x=\frac{1\pm \sqrt{-3}}{2}$
2
To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)
$x=\frac{1+\sqrt{-3}}{2},\:x=\frac{1-1\cdot \sqrt{-3}}{2}$
Final Answer
$x=\frac{1+\sqrt{-3}}{2},\:x=\frac{1-1\cdot \sqrt{-3}}{2}$