Find roots of polynomial $$ p(x) = n^2-n+1 $$
Answer
The roots of polynomial $ p(n) $ are:
$$ \begin{aligned}n_1 &= \frac{ 1 }{ 2 }+\frac{\sqrt{ 3 }}{ 2 }i\\[1 em]n_2 &= \frac{ 1 }{ 2 }- \frac{\sqrt{ 3 }}{ 2 }i \end{aligned} $$Explanation
The solutions of $ n^2-n+1 = 0 $ are: $ n = \dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 3 }}{ 2 }i ~ \text{and} ~ n = \dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 3 }}{ 2 }i$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.
This page was created using
Polynomial Roots Calculator