# Math Help - [SOLVED] Solve the inequality 2x^2 - 5x + 2 ? 0

1. ## [SOLVED] Solve the inequality 2x^2 - 5x + 2 ? 0

Question:
Solve the inequality $2x^2 - 5x + 2 \leq 0$

Attempt:

$2x^2 - 5x + 2 \leq 0$

$2 [ x^2 - \frac{5x}{2} + \frac{2}{2} ]$

$2 [ x^2 - 2.5x + 1 ]$

$2 [ (x - \frac{2.5}{2})^2 - (\frac{2.5}{2})^2 + 1 ]$

$2 [ (x - \frac{2.5}{2})^2 + 2\frac{9}{16} ]$

What to do next?

2. $
\begin{gathered}
x_{1,2} = \frac{{5 \pm \sqrt {25 - 16} }}
{4} = 2,\frac{1}
{2} \hfill \\
\hfill \\
\to 2x^2 - 5x + 2 = 2\left( {x - 2} \right)\left( {x - \frac{1}
{2}} \right) \hfill \\
\end{gathered}
$

thus:

$
\frac{1}
{2} \leqslant x \leqslant 2
$