Find roots of polynomial $$ p(x) = 3x^2-x-83x^2-x-8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -\frac{ 1 }{ 80 }+\frac{ 3 \sqrt{ 71}}{ 80 }i\\[1 em]x_2 &= -\frac{ 1 }{ 80 }-3 \frac{\sqrt{ 71 }}{ 80 }i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ \color{blue}{3x^2} \color{red}{-x} \color{blue}{-83x^2} \color{red}{-x} -8 = \color{blue}{-80x^2} \color{red}{-2x} -8 $$Step 2:
The solutions of $ -80x^2-2x-8 = 0 $ are: $ x = -\dfrac{ 1 }{ 80 }+\dfrac{ 3 \sqrt{ 71}}{ 80 }i ~ \text{and} ~ x = -\dfrac{ 1 }{ 80 }-\dfrac{ 3 \sqrt{ 71}}{ 80 }i$.
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