Question
Find roots of polynomial $$ p(x) = 2-2x+2x^2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= \dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 3 }}{ 2 }i\\[1 em]x_2 &= \dfrac{ 1 }{ 2 }- \dfrac{\sqrt{ 3 }}{ 2 }i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 2-2x+2x^2 & = 0\\[1 em] 2x^2-2x+2 & = 0 \end{aligned} $$Step 2:
The solutions of $ 2x^2-2x+2 = 0 $ are: $ x = \dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 3 }}{ 2 }i ~ \text{and} ~ x = \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