Question

Calcule as Raízes das funções de 2o Grau.
a) F(x) = x2 – 5x + 4
b) F(x) = x2 – 4x + 3
c) F(x) = -x2 + 4x – 3
d) F(x) = x2 + 5x + 4
e) F(x) = x2 – 3x
f) F(x) = -x2 + 2x + 3
g) F(x) = x2 – 25
h) F(x) = x2 - 49

Answer 1

Resposta:

"

Calcule as Raízes das funções de 2°

Grau" .

a) F(x) = x^2 – 5x + 4

"a=1; b = - 5; c = 4'

"∆= b²-4ac"

'∆= (-5)²-4.1.4'

'∆=25-16"

"∆= 9"

"x = (-b +/- √∆)/ 2a"

"x= (5 +/- 3)/2"

"x = (5+3)/2 = 8/2= 4"

"x = (5-3)/2 = 2/2= 1"

R.: s= {1,4}

_________________

b) F(x) = x^2 - 4x + 3

"a = 1; b = - 4; c = 3"

∆= b²-4ac

∆= (-4)²-4.1.3

"∆= 16-12"

"∆= "4"

x = (-b +/- √∆)/2a

x = (4 +/-2)/2

"x= (4+2)/2= 6/2=3"

*x =(4-2)/2=2/2= 1"

:

R.: s ={1,3}

___________________

c) F(x) = - x^2 + 4x – 3

"a= - 1; b = 4; c = - 3"

∆= b²-4ac

∆= (4)² -4.(-1).(-3)

∆= 16-12

"∆ =4 "

x = (-b +/- √∆)/2a

x = (-4+/-2)/2.(-1)

x' = (-4+2)/(-2) = -2/(-2) = +1

x" = (-4-2)/(-2)=-6/(-2) = +3

R.: S= {1,3}

=========

d) F(x) = x^2 + 5x + 4

"a=1; b =5; c = 4"

∆= b²-4ac

∆= 5²-4.1.4

∆= 25-16

"∆=9 "

x = (-5 +/- 3)/2.1

x' = (-5-3)/2= -8/2= - 4"

x" = (-5 +3)/2= -2/2= -1"

_______________

e) F(x) = x^2 – 3x

"x² - 3x =0 "

x.(x-3) = 0'

"x = 0'

"x - 3=0"

"x = 3"

R.: s = {0,3}

______________

f) F(x) = - x^2 + 2x + 3

"a= -1; b =2; c= 3"

"∆= 2² -4.(-1).3"

"∆= 4+12"

"∆=16"

x = (- b +/- √∆)/2.a

x = (-2 +/- √16)/(-2)

x = (-2 +/- 4)/(- 2)

x'' = (-2-4)/-2 = -6/(-2) = +3

x" = (-2+4)/(-2) = 2/(-2) = -1

________________

g) F(x) = x^2 – 25

"x²-25=0"

"x²=25"

*x=√25"

"x = +/- 5 "

R.: {+5; -5}

____________

h) F(x) = x^2 - 49

"x²-49=0"

"x²=49'

"x =√49"

x=+/-7"

R.: s= {+7, -7}