Prove that odd polynomials have at least one root.
13981
Proof that every polynomial of odd degree has one real root
89354
Polynomials, prove exercise question about question
18953
Prove that even + odd is odd.
127547
Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
115834
Cubic polynomial with three (distinct) irrational roots
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
62134
Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
2705
How many roots have modulus less than $1$?
2408
Show that a polynomial has at least one positive solution/root.
103552
The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
139305
Prove $f=1+x+x^2+x^3+\cdots+x^n$ has no multiple roots.
142724
Prove that for all integers $x$ and $y$, $x - y$ is odd if and only if $x + y$ is odd.
51804
How to show that a root of the equation $x (x+1)(x+2) ....... (x+2009) = c $ can have multiplicity at most 2?
44182
Proving that an integer is even if and only if it is not odd
2614
Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$
13656
Prove existence of a real root.
6582
Prove the existence of the square root of $2$.