Proving a polynomial has a solution in the interval (0,1)
25981
Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$
100862
Polynomials with rational zeros
155559
Quickest way to determine a polynomial with positive integer coefficients
12079
A positive polynomial is the sum of two squares in $\mathbb{R}[X]$
61640
Prove c exists for f:[0,1] -> R
129653
Solving a polynomial with grouping
99737
Using Rouché's theorem to find a compact domain for the roots of a polynomial
82567
Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
45811
How to prove that r is a double root if and only if it is a root of a polynomial and of its derivative.
111569
Property of a polynomial with no positive real roots
129646
Defining a function that completes the square given a quadratic polynomial expression
62134
Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
56127
Prove a function is constant under certain conditions
6484
Polynomials in one variable with infinitely many roots.
106868
Prove that $x+\frac1{4x} ≥ 1$ for $x>0$
118085
complex polynomial satisfying inequality
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$