Question

Questão 5- Determine os valores reais de x para os quais (x2 – 8x +12) * (x2 – 5x) < 0.

Answer 1

Resposta:

(x² - 8x +12) * (x² - 5x) < 0

p=x² - 8x +12 ..raízes x'=2 e x''=6  ..a=1>0 ==>concavidade p/cima

p++++++++++++++(2)---------------------(6)+++++++++++++++++++

q=x²-5x ..raízes x'=0  e x''=5 ..a=1>0 ==>concavidade p/cima

q++++++++++++++++++(0)------------------------------(5)+++++++++++++++++

Estudo de Sinais:

p++++++++++++(2)-----------------(6)+++++++++++++++++++++++++

q++++++(0)----------------------------------------(5)+++++++++++++++++

p*q++++(0)------(2)++++++++++(6)---------(5)+++++++++++++++++++

0 < x < 2  U  6 < x < 5

ou

x ∈ Reais  |   (0 , 2) U  (6,5)