Proving that not all roots of a cubic polynomial are real
69575
If $ad$ and $bc$ are odd and even, respectively, then prove that $ax^3+bx^2+cx+d$ has an irrational root.
155575
Proving a polynomial $f(x)$ composite for infinitely many $x$
97652
Can every real polynomial be factored up to quadratic factors?
18702
If $ax^2+(c+b)x+e+d=0$ has real roots greater than $1$, show that $ax^4+bx^3+cx^2+dx+e$ has at least one real root
118916
How do I prove that a polynomial F[x] of degree n has at most n roots
83363
Finding the real root of a cubic algebraically
78379
Proof on cubic residues
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 $\log_5 {abc}\geq2$
40994
How to check that a cubic polynomial is irreducible?
73478
Show that the equation $a_1e^{\alpha_1x} + a_2e^{\alpha_2x} + \cdots + a_ne^{\alpha_nx} = 0$ has at most $n - 1$ real roots.
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.
82567
Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
40014
A polynomial that is zero on an open set
2408
Show that a polynomial has at least one positive solution/root.
139614
Polynomial bounded real part of an entire function
112334
Real roots of a polynomial of real co-efficients , with the co-efficients of $x^2 , x$ and the constant term all $1$