Question

 O conjunto solução da inequação x² – 2x – 3 ≤ 0 é: 

a) {x R/ -1 < x < 3}
b) {x R/ -1 < x ≤ 3}
c) {x R/x < -1 ou x > 3}
d) {x R / -1 ≤ -1 ou ≥ 3}
e) {x R/ -1 ≤ x ≤ 3} ​

Answer 1

$\boxed{\begin{array}{l}\sf x^2-2x-3\leqslant0\\\underline{\rm fac_{\!\!,}a}\\\sf f(x)=x^2-2x-3\\\underline{\rm Ra\acute izes~de~f(x):}\\\sf x^2-2x-3=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-2)^2-4\cdot1\cdot(-3)\\\sf\Delta=4+12\\\sf\Delta=16\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-(-2)\pm\sqrt{16}}{2\cdot1}\\\\\sf x=\dfrac{2\pm4}{2}\begin{cases}\sf x_1=\dfrac{2+4}{2}=\dfrac{6}{2}=3\\\\\sf x_2=\dfrac{2-4}{2}=-\dfrac{2}{2}=-1\end{cases}\\\sf f(x)>0~p/~x<-1~ou~x>3\\\sf f(x)<0~p/-1<x<3\end{array}}$

$\huge\boxed{\boxed{\boxed{\boxed{\sf S=\{x\in\mathbb{R}/-1\leqslant x\leqslant3\}}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~e}}}}$