Question

Determine o Valor da Incognita.

a) 12x2 - 18x=0

b) 25x2+15x=0

c) 27x2 - 3x=0

d) x2 - 7x+10=0

e) x2 - 5x+6=0

Answer 1

Determine o Valor da Incognita.

a) 12x2 - 18x=0

12x² - 18x = 0    ( equação INCOMPLETA)

6x(2x - 3) = 0

6x = 0
x = 0/6
x = 0
e
(2x - 3) = 0
2x - 3 = 0
2x = + 3
x = 3/2

assim
x ' = 0
x " = 3/2

b) 25x2+15x=0

25x² + 15x = 0
5x(5x + 3) = 0

5x = 0
x =0/5
x = 0
e
(5x + 3) = 0
5x + 3 = 0
5x = - 3
x = - 3/5

assim
x' = 0
x" = - 3/5

c) 27x2 - 3x=0

27x² - 3x = 0
3x(9x - 1) = 0

3x = 0
x = 0/3
x = 0
e
(9x - 1)- 0
9x - 1 = 0
9x = + 1
x = 1/9

assim
x' = 0
x" = 1/9

d) x2 - 7x+10=0

x² - 7x + 10 = 0
ax² + bx + c = 0
x² - 7x + 10 = 0
a = 1
b = - 7
c = 10
Δ = b² - 4ac
Δ = (-7)² - 4(1)(10)
Δ = + 49 - 40
Δ = + 9 ---------------------> √Δ = 9   ( porque √9 = 3)
se
Δ > 0 ( DUAS raizes diferentes)
(baskara)

           - b + - √Δ
x = -------------------
                2a

x' = -(-7) - √9/2(1)
x' = + 7 - 3/2
x' = + 4/2
x' = 2
e
x" = - (-7) + √9/2(1) 
x" = + 7 + 3/2
x" = + 10/2
x" = 5

assim
x' = 2
x" = 5


e) x2 - 5x+6=0

x² - 5x + 6 = 0
a = 1
b = - 5
c = 6
Δ = b² - 4ac
Δ = (-5)² - 4(1)(6)
Δ = + 25 - 24
Δ= + 1 --------------------> √Δ = 1   (porque √1 = 1)
se
Δ > 0 ( DUAS raizes diferentes)
(baskara)

           - b + - √Δ
x = -------------------
                2a

x' = -(-5) - √1/2(1)
x' = + 5 - 1/2
x' = + 4/2
x' = + 2
e
x" = - (-5) + √1/2(1)
x" = + 5 + 1/2
x" = + 6/2
x" = 3

assim
x' = 2
x" = 3