Find roots of polynomial $$ p(x) = x^2+x+2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -\frac{ 1 }{ 2 }+\frac{\sqrt{ 7 }}{ 2 }i\\[1 em]x_2 &= -\frac{ 1 }{ 2 }- \frac{\sqrt{ 7 }}{ 2 }i \end{aligned} $$Explanation
The solutions of $ x^2+x+2 = 0 $ are: $ x = -\dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 7 }}{ 2 }i ~ \text{and} ~ x = -\dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 7 }}{ 2 }i$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.
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