Show that $|z^2| + Re(a \cdot z) +b = 0$ has only solutions for $|a^2|\geq 4b$
140009
Show complex solutions exist
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
94837
Solving complex equation $z^2 + (1+i) \overline{z} + 4i = 0$
65000
prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
91003
Prove that equation has exactly 2 solutions
130327
Prove that $a^2 > b^2$ ; if $a > b \geq 0$.
118467
Prove that $a^2+ab+b^2\ge 0$
41689
Find all solutions: $x^2 + 2y^2 = z^2$
15604
Determine the set of points $z$ that satisfy the condition $|2z|>|1+z^2|$
142725
The general solution of $x^a = a^x$ for real $a >0$
156468
Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
117352
Show $x^n+ax+b=0$ has most two solutions
73079
Eliminating non-integer solutions to $ab / (2\sqrt{ab} + a + b)$
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
57191
Show that if $a>e$, the equation $az^n=e^z$ admit $n$ roots in the unit disk - Rouché theorem
42713
Solutions to the equation $ze^{a-z}=1$