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

  1. #1
    Member looi76's Avatar
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    [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} ]

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  2. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
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    397
    <br />
\begin{gathered}<br />
  x_{1,2}  = \frac{{5 \pm \sqrt {25 - 16} }}<br />
{4} = 2,\frac{1}<br />
{2} \hfill \\<br />
   \hfill \\<br />
   \to 2x^2  - 5x + 2 = 2\left( {x - 2} \right)\left( {x - \frac{1}<br />
{2}} \right) \hfill \\ <br />
\end{gathered} <br />

    thus:

    <br />
\frac{1}<br />
{2} \leqslant x \leqslant 2<br />
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