# Questions tagged [quartics]

Equations that can be written in the form $p(x) = 0$ for a univariate polynomial $p$ of degree $4$ or $p(X_1, \ldots, X_r) = 0$ for a multivariate polynomial $p$ of total degree $4$. Questions that use this tag should usually also have the polynomial tag.

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### Invariants of a quartic function

Some facts about cubic functions and quartic functions motivate this question: Every cubic function $f$ has exactly one inflection point $P$, and the graph $y=f(x)$ is symmetric about $P$. In ...
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### How many roots in a system of quartic equations

I am considering three general tori in 3D space, each defined by a quartic equation. My primary question revolves around the number of real solutions that arise from the system of these three ...
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### Show that the polynomial $P(x):=x^4-6x+6$ has no real roots .

Show that the polynomial $$P(x):=x^4-6x+6$$ has no real roots. We need to solve this problem without using calculus. This is a problem from my son's olympiad textbook. Since the degree of the ...