Disequazione di terzo grado $x^3-4x<0$

Text

Solve the inequality $x^3-4x<0.$

Solution

Factor: $x^3-4x=x(x^2-4)=x(x-2)(x+2)$. The key points are $x=-2,\ 0,\ 2$. Study the sign of the product of the three factors:

• $x<-2$: product $<0$;
• $-2<x<0$: product $>0$;
• $0<x<2$: product $<0$;
• $x>2$: product $>0$. $\boxed{x<-2\ \vee\ 0<x<2.}$