Question

resolva as seguntes inequaçoes do 2 grau a) 3x2-10x+7<0
b) -4x2+9>0

Answer 1

Boa tarde Leticia!


Solução!


$3 x^{2} -10x+7\ \textless \ 0\\\\\\ Aplicando~~a~~formula ~~de~~Bhaskara!\\\\\\ a=3\\\\ b=-10\\\\\ c=7$


$x= \dfrac{-b\pm \sqrt{b^{2}-4.a.c } }{2.a}\\\\\\\\ x= \dfrac{-(-10)\pm \sqrt{(-10)^{2}-4.3.7 } }{2.3}\\\\\\\\ x= \dfrac{10\pm \sqrt{100-84 } }{6}\\\\\\\\ x= \dfrac{10\pm \sqrt{16} }{6}\\\\\\\\ x= \dfrac{10\pm 4 }{6}\\\\\\\\ Raizes!\\\\\ x_{1}= \dfrac{10+4}{6}= \dfrac{14}{6}= \dfrac{7}{3}\\\\\\\ x_{2}= \dfrac{10-4}{6}= \dfrac{6}{6}= 1$

Analisando a desigualdade concluímos.


$\boxed{Resposta:S= \{x \in\mathbb{R}~|~ 1\ \textless \ x\ \textless \ \frac{7}{3}\} }$



$-4 x^{2} +9\ \textgreater \ 0\\\\\ -4 x^{2} \ \textgreater \ -9.(-1)\\\\\ 4 x^{2} \ \textless \ 9\\\\\ x^{2} \ \textless \ \dfrac{9}{4}\\\\\\ x\ \textless \ \sqrt{ \dfrac{9}{4} }\\\\\\\ x\ \textless \ \pm \dfrac{3}{2} \\\\\\\\\\ \boxed{Resposta: S=\{ x \in \mathbb{R}~|~ -\frac{3}{2}\ \textless \ x\ \textless \ \frac{3}{2}\}}$


Boa tarde!

Bons estudos!