Solution assignment 04 Quadratic inequalities

Solve:

$3x^2+x-2\geq0$

First we solve the corresponding equation:

$3x^2+x-2=0$

and use the $abc$ -formula:

$x_{1,2}=\displaystyle\frac{-1\pm\sqrt{1^2-4.3.-2}}{2.3}=\displaystyle\frac{-1\pm5}{6}$

Thus the solutions are:

$x_1=-1$ or $x_2=\displaystyle\frac{2}{3}$

The graph of the function in the left-hand side is an 'opens up' parabola and thus the following values of $x$ satisfy the inequality:

$x\leq{-1}$ or $x\geq\displaystyle\frac{2}{3}$