Find roots of polynomial $$ p(x) = 8+4x+2x^2+4x^3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.1475\\[1 em]x_2 &= 0.3237+1.2799i\\[1 em]x_3 &= 0.3237-1.2799i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 8+4x+2x^2+4x^3 & = 0\\[1 em] 4x^3+2x^2+4x+8 & = 0 \end{aligned} $$Step 2:
Polynomial $ 4x^3+2x^2+4x+8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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