Question

vamos resolver a inequação 3×2+10×+7 <0​

Answer 1

$\Large\boxed{\begin{array}{l}\sf 3x^2+10x+7<0\\\underline{\rm fac_{\!\!,}a}\\\sf f(x)=3x^2+10x+7\\\underline{\rm Ra\acute izes~de~f(x):}\\\sf 3x^2+10x+7=0\\\sf\Delta=b^2-4ac\\\sf\Delta=10^2-4\cdot3\cdot7\\\sf\Delta=100-84\\\sf\Delta=16\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-10\pm\sqrt{16}}{2\cdot3}\\\\\sf x=\dfrac{-10\pm4}{6}\begin{cases}\sf x_1=\dfrac{-10+4}{6}=-\dfrac{6}{6}=-1\\\\\sf x_2=\dfrac{-10-4}{6}=-\dfrac{14\div2}{6\div2}=-\dfrac{7}{3}\end{cases} \end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm Observe~a~figura~que~eu~anexei}\\\sf ~f(x)<0\iff -\dfrac{7}{3}<x<-1\\\sf Portanto\\\sf S=\bigg\{x\in\mathbb{R}/-\dfrac{7}{3}<x<-1\bigg\}\end{array}}$