For any real number $c$, the polynomial $x^3 + x + c$ has exactly one real root For any real number $c$, the polynomial $x^3 + x + c$ has exactly one real root.  
how can i show that above statement is true or false.can anyone help me please

There are several ways to do it:


*

*Show that $x \mapsto x^3+x+c$ is increasing

*Use Rolle's theorem.

*Use Descartes' rule of signs: If $c>0$ it has a negative root while if $c\leq0$ it has a nonnegative root.

