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Results tagged with polynomials
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user 9232
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
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Least positive value of a random polynomial
For $d=2$ the following easy argument shows that the probability, if it exists, is strictly positive: consider the set of polynomials $$ \{f=c_2x^2+c_1x+c_0:0\leq c_1<1/2<c_0,c_2\leq 1 \}$$ that has positive … Each such polynomial has minimum value $$ \frac{-c_1^2+4c_0c_2}{4c_2}\geq \frac{-1/4+1}{4}=\frac{3}{16}>0.$$
Question 2: Now let us focus on the polynomials that only take non-negative values. …
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