Question

Faça o estudo dos sinais e resolva as funções

a) y = x² + 2x

b) f(x) = x² - 7x + 10

c) f(x) = 4 - x²

d) y = 2x² - 3x = 4

e) f(x) = x² + 2x + 1

f) f(x) = 3x² - 7x + 2

Answer 1

$a) \\ y=x^2+2x \\ x^{2} +2x=0 \\ x(x+2)=0 \\ x+2=0~~ ou~~~x=0 \\ x=-2 \\ \\ +++\circ^{-2}---\circ^0+++ \\ \\ y=0~~p/ ~~x=-2~~ ou~~x=0 \\ y\ \textgreater \ 0~~p/~~\{x\in R/ x\ \textless \ -2~~ ou~~x\ \textgreater \ 0\} \\ y\ \textless \ 0~~p/~\{x\in R/-2\ \textless \ x\ \textless \ 0\}$

$b) \\ y=x^2-7x+10 \\ x^2-7x+10=0 \\ (x-5)(x-2)=0 \\ x-5=0~~~~x-2=0 \\ x=5~~~~~~~~~~x=2 \\ \\ +++\circ^2---\circ^5+++ \\ \\ y=0~~p/~~x=2~~ ou~~x=5 \\ y\ \textgreater \ 0~~p/~~\{x\in R/x\ \textless \ 2~~ ou ~~ x\ \textgreater \ 5\} \\ y\ \textless \ 0~~p/~~\{x\in R/2\ \textless \ x\ \textless \ 5\}$


$d) \\ y=4-x^2 \\ 4-x^2=0 \\ -x^2=-4~~~\times(-1) \\ x^{2} =4 \\ x=\pm \sqrt{4} \\ x=\pm2 \\ \\ ---\circ^{-2}+++\circ^2--- \\ \\ y=0~~p/~~x=-2~~ ou~~x=2 \\ y\ \textless \ 0~~p/~~\{x\in R/x\ \textless \ -2~~ ou~~x\ \textgreater \ 2\} \\ y\ \textgreater \ 0~~p/~~\{x\in R/-2\ \textless \ x\ \textless \ 2\}$


$e) \\y= x^2+2x+1 \\ x^{2} +2x+1=0 \\ (x+1)^2=0 \\ x+1=0 \\ x=-1 \\ \\ ++++\circ^{-1}++++ \\ \\ y=0~~p/~~x=-1 \\ y\ \textgreater \ 0~~p/~~\{x\in R/x \neq -1\}$  


$f) \\ y=3x^2-7x+2 \\ 3x^2-7x+2=0 \\ \\ \Delta=7^2-4(3)(2) \\\Delta=49-24 \\ \Delta=25 \\ \\ x= \frac{-(-7)\pm \sqrt{25} }{2.(3)} = \frac{7\pm5}{6} \\ \\ x'= \frac{7+5}{6} =2 \\ \\ x"= \frac{7-5}{6} = \frac{2}{6} = \frac{1}{3} \\ \\ +++\circ^{ \frac{1}{3} }---\circ^2+++ \\ \\ y=0~~p/~~x= \frac{1}{3} ~~~ou~~ x=2 \\ \\ y\ \textgreater \ 0~~p/~~\{x\in R/\ \textless \ \frac{1}{3} ~~ ou~~x\ \textgreater \ 2\} \\ \\ y\ \textless \ 0~~p/~~\{x\in R/ \frac{1}{3} \ \textless \ x\ \textless \ 2\}$

Answer 2

Resposta:

Explicação passo-a-passo:

f(x) X²-4x-5