For polynomial with degree 3, when $a + ib$ is a root show $a-ib$ is a root, and it also has a rational root.
70203
If an polynomial has a complex root, is it necessary that its conjugate is also a root?
156034
sufficient condition for a polynomial to have roots in $[0,1]$
144769
Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$
41073
Prove $ax^2+bx+c=0$ has no rational roots if $a,b,c$ are odd
56697
How to show that the given equation has at least one complex root ,a s.t |a|>12
13981
Proof that every polynomial of odd degree has one real root
44247
For $a^3+b^3+c^3=3$ prove that $a^4b+b^4c+c^4a\leq3$
141184
Proof that a degree 4 polynomial has at least two roots
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
51804
How to show that a root of the equation $x (x+1)(x+2) ....... (x+2009) = c $ can have multiplicity at most 2?
62134
Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
2408
Show that a polynomial has at least one positive solution/root.
30622
Proving $\sqrt 3$ is irrational.
127056
How to prove that a polynomial of degree $n$ has at most $n$ roots?
140481
How to tell if a quartic equation has a multiple root.
122487
Degree of Rational Function