$$x^4-\frac{1}{2}x^3-\frac{1}{2}x+1 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.84307+0.5378i & x_2 = 0.84307-0.5378i & x_3 = -0.59307+0.80515i \\[1 em] x_4 = -0.59307-0.80515i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^4-\frac{1}{2}x^3-\frac{1}{2}x+1 &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x^4-2 \cdot \frac{1}{2}x^3-2\frac{1}{2}x+2\cdot1 &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]2x^4-x^3-x+2 &= 0&& \\[1 em] \end{aligned} $$
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