Given a polynomial of degree $n$, and the possible coefficients of polynomials are restricted to an interval for each of the degree. Is there a way to estimate number of roots of this polynomial in a given interval $[x_1,x_2]$.
Polynomial roots in an interval for coefficients spanning a subspace of $\mathbb{R}^n$
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polynomials
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0By "polynomial of order n", do you mean degree n? That is, your polynomial is $a_n x^n + \dots + a_1 x + a_0$? – 2011-11-24
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2Given an interval $[x_1,x_2]$ you can check if $f(x_1) f(x_2) <0$ and in this case you can deduce there exists at least one root of the polynomial in the interval. If $f'(x)<0$ or $f'(x) >0$ for every $x \in [x_1,x_2]$ then the root is unique. – 2011-11-24
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0To Dimitrije Kostic: Ya order I meant degree. – 2011-11-24
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0Do you mean to impose different conditions on each $a_i$, or the same condition on all of the $a_i$? – 2013-06-12
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0@DylanYott Question isn't mine, but I read "an interval for each of the degree[s]" as having an interval for each $a_i$. – 2013-06-12