Find roots of polynomial $$ p(x) = 5x^3-x^4+25x^2+2x+6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -3.0885\\[1 em]x_2 &= 8.1203\\[1 em]x_3 &= -0.0159+0.4889i\\[1 em]x_4 &= -0.0159-0.4889i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 5x^3-x^4+25x^2+2x+6 & = 0\\[1 em] -x^4+5x^3+25x^2+2x+6 & = 0 \end{aligned} $$Step 2:
Polynomial $ -x^4+5x^3+25x^2+2x+6 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
This page was created using
Polynomial Roots Calculator