$$4x^3-8x^2+7x-\frac{11}{2}x+1 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.25983 & x_2 = 0.56908 & x_3 = 1.69075 \end{matrix} $$
Explanation
$$ \begin{aligned} 4x^3-8x^2+7x-\frac{11}{2}x+1 &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot4x^3-2\cdot8x^2+2\cdot7x-2 \cdot \frac{11}{2}x+2\cdot1 &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]8x^3-16x^2+14x-11x+2 &= 0&& \text{simplify left side} \\[1 em]8x^3-16x^2+3x+2 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
This page was created using
Polynomial Equations Solver