Question

12-) utilizando a formula resolutiva resolva as seguintes equações do 2 ° grau sendo U = IR.

Answer 1

10)
a) 4x² - 12x = 0
    4x( x - 3) = 0
x1 = 0/4 = 0
x2 = 0 + 3 = 3

b) 3x² - 75 = 0
    3x² = 75
      x² = 25
      x = +/- 5

c) x² - 3 = 0
x² = 3
x = √3

d) 5x² -20x = 0
    5x(x - 4) = 0
    x1 = 0
    x2 = 4

e) x² + 1= 0 
   x² = -1
  x = √-1    impossível

11) 
a) 3x² - 5x + 3 = 0
Δ = (-5)² - (4.3.3)
Δ = 25 - 36
Δ = 11 (2 raizes)

b) 2x² -3x + 1 = 0
Δ= 9 - 8
Δ = 1 (2 raizes)

c) 5x² -x -1 = 0
Δ = 1 _ 20
Δ = -19  nenhuma raiz

d) x² -7x +10 =0
Δ = 49 - 40
Δ = 9 ( 2 raizes)

12) 
a) 2x² - 3x + 1=0
x = (3 +/- √9 - 8) ÷ 2
x = (3 +/- √1) ÷ 2
x1 = (3 + 1) ÷ 2 = 2
x2 = (3 - 1) ÷ 2 = 1

b) x² - 2x - 3 = 0
x = (2 +/-√4 +12) ÷ 2
x = (2 +/- √16) ÷ 2
X1 = ( 2 + 4) ÷ 2 = 3
X2 = (2 - 4 ) ÷ 2 = -1

c) x² - 4x - 2 = 0
x = (4 +/- √16 + 8) ÷ 2
X = (4 +/- √24) ÷ 2
X1 = (4 + 2√6) ÷ 2 = 2 + √6
X2 = (4 - 2√6) ÷ 2 =  2 - √6

d) x² + x + 2 = 0
x = (-1 +/-√1 - 8) ÷ 2
X = (-1 +/- √-7) ÷ 2 IMPOSSÍVEL

13)
a) x² - 8x + 15
x1 + x2 = - b/a = 8/1 = 8
x1 . x2 = c/a = 15/1 = 15

b) 3x² - 6x = 0
x1 + x2 = 6/3 = 2
x1 . x2 = 0/1 = 0

c) 2x² -7x + 6 = 0
x1 + x2 = 7/2 = 3,5
x1 . x2 = 6/2 = 3

d) 5x² - 10x + 6 = 0
x1 + x2 = 10/5 = 2
x1 . x2 = 6/5 = 1,2