Find roots of polynomial $$ p(x) = 1-16x+30x^2-64x^3-212x^4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.07\\[1 em]x_2 &= -0.6845\\[1 em]x_3 &= 0.1563+0.2721i\\[1 em]x_4 &= 0.1563-0.2721i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 1-16x+30x^2-64x^3-212x^4 & = 0\\[1 em] -212x^4-64x^3+30x^2-16x+1 & = 0 \end{aligned} $$Step 2:
Polynomial $ -212x^4-64x^3+30x^2-16x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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