From Equation (I), we found that one root is x=- 1. To find other roots, we will solve Equation (II). Note that this is a quadratic equation. Thus, we will use the Quadratic Formula.
ax^2+bx+c=0
⇕
x=- b±sqrt(b^2-4ac)/2a
To do so, we first need to identify a, b, and c.
x^2-x+1=0
⇕
1x^2+( - 1)x+ 1=0
We see that a= 1, b= - 1, and c= 1. Let's substitute these values into the formula and evaluate the right-hand side. Remember that sqrt(- a)= isqrt(a).
These roots of the quadratic equation are also roots of the given equation.
Roots
x=- 1, x=1 ± isqrt(3)/2
There are three roots. One of these roots is real and two of them are imaginary.
