Show that $X^3+X^2+1$ has only one real root
130823
cubic equations which have exactly one real root
19355
prove $f(x)=x^3+x$ is one to one and onto
39270
Showing that $e^x > 1+x$
157487
Showing a polynomial having at least one integer root under certain conditions has precisely one integer root
109288
Prove that $x^3+y^3+z^3-3xyz=1$ defines a surface of revolution
109760
Showing that the product of all $n$th Roots of Unity is $(-1)^{n+1}$
126445
Proving the second root of a quadratic equation
120457
Show that the equation, $x^3+10x^2-100x+1729=0$ has at least one complex root $z$ such that $|z|>12.$
128575
Elementary proof that $3$ is a primitive root of a Fermat prime?
7279
$|2^x-3^y|=1$ has only three natural pairs as solutions
61987
$x^2+1=0$ in $\mathbb{Z}_7$
83363
Finding the real root of a cubic algebraically
112334
Real roots of a polynomial of real co-efficients , with the co-efficients of $x^2 , x$ and the constant term all $1$
154393
Roots of polynomial with real coefficients appear in conjugate pairs.
69618
What is the sum of non-real roots of the polynomial equation?
28502
How to solve $x^3=-1$?
107765
Prove that there exists two roots in $[-1,1]$