Find roots of polynomial $$ p(x) = x^4-12x^3+12x^2+208-384 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -2.0691\\[1 em]x_2 &= 11.0441\\[1 em]x_3 &= 1.5125+2.3269i\\[1 em]x_4 &= 1.5125-2.3269i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^4-12x^3+12x^2+ \color{blue}{208} \color{blue}{-384} = x^4-12x^3+12x^2 \color{blue}{-176} $$Step 2:
Polynomial $ x^4-12x^3+12x^2-176 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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