Question
$$\frac{1}{4}k^4+2k^3+\frac{5}{2}k^2+k+6 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{1}{4}k^4+2k^3+\frac{5}{2}k^2+k+6 &= 0&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1}{4}k^4+4\cdot2k^3+4\frac{5}{2}k^2+4k+4\cdot6 &= 4\cdot0&& \text{cancel out the denominators} \\[1 em]k^4+8k^3+10k^2+4k+24 &= 0&& \\[1 em] \end{aligned} $$
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