Question

Resolva as equações de 2ºGrau:
6x²+x-1=0
3x²-7x+2=0
2x²-7x=15

Answer 1

a)
6x²+x-1 = 0
/\ = 1² - 4.6.(-1)
/\ = 1 + 24
/\ = 25
x = (-1+/-\/ 25)/2.6
x = (-1+/-5)/12
x' = (-1+5)/12 = 4/12 = 4:4/12:4 = 1/3
x" = (-1-5)/12 = -6/12 = -1/2

b) 
3x²-7x+2 = 0
/\ = (-7)²-4.3.2
/\ = 49 - 24
/\ = 25
x  = [-(-7)+/-\/ 25]/2.3
x = (7+/-5)/6
x' = (7+5)/6 = 12/6 = 2
x" = (7-5)/6 = 2/6 = 1/3

c)
2x² - 7x = 15
2x² - 7x - 15 = 0
/\ = (-7)² - 4.2.(-15)
/\ = 49 + 120
/\ = 169
x = [-(-7)+/-\/ 169]/2.2
x = (7+/-13)/4
x' = (7+13)/4 = 20/4 = 5
x' = (7-13)/4 = -6/4 = -3/2

Answer 2

a)
6x² + x - 1 = 0
a = 6; b = 1; c = - 1

Δ = b² - 4ac
Δ = 1² - 4.6.(- 1)
Δ = 1 + 24
Δ = 25

x = - b +/- √Δ = - 1 +/- √25
           2a               2.6

x = - 1 + 5 =  4  (:4)    =  1
          12      12  (:4)       3

x = - 1 - 5 = - 6  (:6) = - 1
         12       12 (:6)      2
------------------------------------------------------------
b)
3x² - 7x + 2 = 0
a = 3; b = - 7; c = 2

Δ = b² - 4ac
Δ = (-7)² - 4.3.2
Δ = 49 - 12.2
Δ = 49 - 24
Δ = 25

x = - b +/- √Δ = - ( - 7) +/- √25
            2a                2.3

x = 7 + 5 = 12 = 2
         6        6

x = 7 - 5 =  2  (:2) =   1
         6       6  (:2)      3
----------------------------------------------
c)
2x² - 7x = 15
2x² - 7x - 15 = 0
a = 2; b = - 7; c = - 15

Δ = b² - 4ac
Δ = (-7)² - 4.2.(-15)
Δ = 49 + 8.15
Δ = 49 + 120
Δ = 169

x = - b +/- √Δ = - ( - 7) +/- √169
           2a                   2.2

x = 7 + 13 = 20 =  5
         4          4

x = 7 - 13 = - 6 (:2) =  - 3
         4         4  (:2)      2