If $r(x)$ is an $n$th degree polynomial of the form $r(x) = a_0+a_1x+\cdots+a_nx^n$ with $n$ odd, prove that $r(x)$ has at least one real root
13981
Proof that every polynomial of odd degree has one real root
143321
Number of roots of a polynomial over a finite field
56697
How to show that the given equation has at least one complex root ,a s.t |a|>12
48260
If $R=K[X]/(X^n)$, can represent any element as polynomial with degree $<n$
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
114872
If $ax^2-bx+c=0$ has two distinct real roots lying in the interval $(0,1)$ $a,b,c$ belongs to natural prove that $\log_5 {abc}\geq2$
141983
Complex polynomial of degree $n$
94682
Polynomial: prove there is no double root
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
82567
Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
109760
Showing that the product of all $n$th Roots of Unity is $(-1)^{n+1}$
7199
Suppose that $P(x)$ is a polynomial of degree $n$ such that $P(k)=\dfrac{k}{k+1}$ for $k=0,1,\ldots,n$. Find the value of $P(n+1)$
155575
Proving a polynomial $f(x)$ composite for infinitely many $x$
154507
If all the roots of a polynomial P(z) have negative real parts, prove that all the roots of P'(z) also have negative real parts
109721
The number of zeros in a polynomial
49899
Determine the number of real roots