Question

escreva a equação na forma A×2+b×+c=0, sabendo-se que :

Answer 1

a)
s = 8
P = 15

x' + x" = 8
3 + 5 = 8

x'.x" = 15
3.5 = 15

x^2 + Sx - p = 0
(x - x').(x - x") = 0
(x - 3).(x - 5) = 0
x^2 - 5x - 3x + 15 = 0

x^2 - 8x + 15 = 0

a = 1; b = - 8; c = 15
∆= b^2-4ac
∆ = (-8)^2 - 4.1.15
∆ = 64 - 60
∆ = 4
x = [ - b +/- √∆]/2a
x = [ -(-8)+/- √4]/2.1
x = [8 +/- 2]/2
x' = [8+2]/2 = 10/2 = 5
x " = [8 - 2]/2 =6/2 = 3

R.: x^2 - 8x + 15 = 0

b)
S = 3
P = - 10

S = x' + x" = 5 +(-2) = 3
P = x'.x" = 5.(-2) = - 10

5 e - 2

(x - x').(x - x") = 0
(x - 5).[x -(-2)] = 0

(x - 5).(x + 2) = 0
x^2 + 2x - 5x - 10 = 0
x^2 - 3x - 10 = 0
a = 1; b = - 3; c = - 10
∆ = b^2-4ac
∆ = (-3)^2 - 4.1.(-10)
∆ = 9 + 40
∆ = 49

x = [ - b +/- √∆]/2a
x = [ -(-3) +/- √49]/2.1
x' = [ 3 + 7]/2 = 10/2 = 5
x" = [ 3 - 7]/2 = - 4/2 = - 2

R : x^2 - 3x - 10 = 0