query: Prove regarding number of distinct polynomial roots
positive_passages.docid: 143321
positive_passages.text: Number of roots of a polynomial over a finite field
negative_passages.docid: 69523
negative_passages.text: Prove that polynomial of degree $4$ with real roots cannot have $\pm 1$ as coefficients (IITJEE)
negative_passages.docid: 25290
negative_passages.text: Determine the number of irreducible monic polynomials of degree 3 in $\mathbb F_p[x]$
negative_passages.docid: 140412
negative_passages.text: If $p$ and $q$ are distinct primes such that $p|c$ and $q|c$, prove that $pq|c$
negative_passages.docid: 42265
negative_passages.text: A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
negative_passages.docid: 45811
negative_passages.text: How to prove that r is a double root if and only if it is a root of a polynomial and of its derivative.
negative_passages.docid: 89354
negative_passages.text: Polynomials, prove exercise question about question
negative_passages.docid: 76482
negative_passages.text: Closure of the set of degree $n$ polynomials with $n$ real roots
negative_passages.docid: 154393
negative_passages.text: Roots of polynomial with real coefficients appear in conjugate pairs.
negative_passages.docid: 33011
negative_passages.text: Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
negative_passages.docid: 144769
negative_passages.text: Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$
negative_passages.docid: 107765
negative_passages.text: Prove that there exists two roots in $[-1,1]$
negative_passages.docid: 77820
negative_passages.text: Roots in a polynomial ring
negative_passages.docid: 120629
negative_passages.text: Prove if $n$ has a primitive root, then it has exactly $\phi(\phi(n))$ of them
negative_passages.docid: 158063
negative_passages.text: A formula for the roots of a solvable polynomial
negative_passages.docid: 82567
negative_passages.text: Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
negative_passages.docid: 24000
negative_passages.text: Roots of Sum of Two Polynomials (with Known Roots)