Question

cum se rezolva 2x2-3x-2mai mare decit 0

Answer 1

[tex]2 \cdot 2 - 3x -2 \ \textgreater \ 0 \\ 4 - 3x-2\ \textgreater \ 0 \\ 2-3x\ \textgreater \ 0 \\ -3x\ \textgreater \ -2 | \cdot (-1) \\ 3x\ \textless \ 2 \\ x\ \textless \ \frac{2}{3} [/tex]
x ∈ (-∞; $\frac{2}{3}$)

Answer 2

$2x^2-3x-2 \ \textgreater \ 0 \\\\ \hbox{Aflam radacinile inecuatiei de gradul II egaland ecuatia cu 0} \\\\ 2x^2-3x-2=0 \\\\ a=2 \\ b=-3\\c=-2 \\\\ \Delta=b^2-4ac \to(-3)^2-4*2*(-2)=9+16 \to \boxed{25} \\\\ x_1;x_2=\frac{-b\pm \sqrt{\Delta}}{2a}\to \frac{3\pm \sqrt{25}}{2*2}= \frac{3\pm 5}{4} \\\\\\ x_1=\frac{3+5}{4}= \frac{\not 8}{\not 4} \to \boxed{2} \\\\\\ x_2=\frac{3-5}{4}= \frac{-2}{4} \to \boxed{-\frac{1}{2}}$

$\hbox{Facem tabelul semnelor:}$
 
         x            | -∞             $-\frac{1}{2}$           2           +∞
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2x² -3x -2       |++++++++++ O ------ O ++++++++++



$S \in (-\infty; -\frac{1}{2}) \cup (2; + \infty)$