Disequazione di secondo grado $3x^2-5x-2>0$

Text

Solve the inequality $3x^2-5x-2>0.$

Solution

The roots of the trinomial come from the quadratic formula: $x=\frac{5\pm\sqrt{25+24}}{6}=\frac{5\pm 7}{6}\implies x=-\tfrac13,\ x=2.$ The parabola $y=3x^2-5x-2$ opens upward, so it is positive outside the interval between the roots: $\boxed{x<-\tfrac13\ \vee\ x>2.}$