Question
$$\frac{1}{8}x^4+\frac{5}{2}x^2 = 3$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{1}{8}x^4+\frac{5}{2}x^2 &= 3&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8 \cdot \frac{1}{8}x^4+8\frac{5}{2}x^2 &= 8\cdot3&& \text{cancel out the denominators} \\[1 em]x^4+20x^2 &= 24&& \text{move all terms to the left hand side } \\[1 em]x^4+20x^2-24 &= 0&& \\[1 em] \end{aligned} $$
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