$$x^4+3x^3+x^2+2x+1 = x+2$$
Answer
$$ \begin{matrix}x_1 = 0.458 & x_2 = -2.81578 & x_3 = -0.32111+0.81994i \\[1 em] x_4 = -0.32111-0.81994i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^4+3x^3+x^2+2x+1 &= x+2&& \text{move all terms to the left hand side } \\[1 em]x^4+3x^3+x^2+2x+1-x-2 &= 0&& \text{simplify left side} \\[1 em]x^4+3x^3+x^2+x-1 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
This page was created using
Polynomial Equations Solver