Question

Dada a funçao quadratica g(x) = x² + 7 - 10x, determine x de modo que g(x) = -2.

Answer 1

g(x) = x² - 10x + 7

g(x) = -2

x² - 10x + 7 = -2
x² - 10x + 7 + 2 = 0
x² - 10x + 9 = 0

Δ = (-10)² - 4.(1).(9)
Δ = 100 - 36
Δ = 64

x = $\frac{-(-10)^+_-\sqrt{64}}{2.(1)}$

x = $\frac{10^+_-8}{2}$


x' = $\frac{10 \ + \ 8}{2}$

x' = $\frac{18}{2}$

x' = 9


x" = $\frac{10 \ - \ 8}{2}$

x" = $\frac{2}{2}$

x" = 1


$\boxed{\bold{S = (1, 9)}}$

Answer 2

$g(x)=x^2-10x + 7$

Se g(x) = -2 , então:

$x^2-10x+7=-2 \\ \\ x^2-10x+7+2=0 \\ \\ x^2-10x+9=0$

Resolvendo a equação:

$x = \frac{-(-10)\pm \sqrt{(-10)^2-4\cdot1\cdot9} }{2} \\ \\ x= \frac{10\pm \sqrt{64} }{2} \\ \\ x= \frac{10\pm8}{2} \\ \\ \\ x'= \frac{10+8}{2} \rightarrow \boxed{x'=9} \\ \\ x''= \frac{10-8}{2} \rightarrow \boxed{x''=1}$

Portanto, para g(x) = -2 , temos os seguintes valores de x:

x' = 9
x'' = 1