Question
$$x^4-4x^3+6x^2-4x+1 = \frac{1}{5}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^4-4x^3+6x^2-4x+1 &= \frac{1}{5}&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5x^4-5\cdot4x^3+5\cdot6x^2-5\cdot4x+5\cdot1 &= 5\cdot\frac{1}{5}&& \text{cancel out the denominators} \\[1 em]5x^4-20x^3+30x^2-20x+5 &= 1&& \text{move all terms to the left hand side } \\[1 em]5x^4-20x^3+30x^2-20x+5-1 &= 0&& \text{simplify left side} \\[1 em]5x^4-20x^3+30x^2-20x+4 &= 0&& \\[1 em] \end{aligned} $$
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