Question

Resolva as seguintes equações do 2º grau, identifique os coeficientes e determine as raízes se existir; através da fórmula de Bhaskara.

a) 2x² - 7x = 15 b) 4x² + 9 = 12x c) x² = x + 12 d) 2x² = -12x - 18 e) x² + 9 = 4x f) 25x² = 20x – 4 g) 4x² - x + 1 = x + 3x² h) 3x² + 5x = -x – 9 + 2x² i) 4 + x ( x - 4) = x j) x ( x + 3) – 40 = 0

Answer 1

Resposta:

a) 2x² - 7x = 15    ...a=2,b=-7 e c=-15

2x²-7x-15=0

x'=[7+√(49+120)]/4=(7+13)/4=5

x''=[7-√(49+120)]/4=(7-13)/4=-6/4

b) 4x² + 9 = 12x  ...a=4 ..b=-12 e c=9

4x²-12x+9=0

x'=x''=[12+√(144-144)]/8=12/8=3/4

c) x² = x + 12     ...a=1, b=-1 e c=-12

x²-x-12=0

x'=[1+√(1+48)]/2=(1+7)/2=4

x''=[1-√(1+48)]/2=(1-7)/2=-3

d) 2x² = -12x - 18    ...a=2 , b=12 e c=18

2x²+12x+18=0

x'=x''=[-12+√(144-144)]/4=-12/4=-3

e) x² + 9 = 4x    ...a=1  , b=-4  e c=9

x²-4x+9=0

Δ=16-36 < 0 ...ñ tem raízes

f) 25x² = 20x – 4    ...a=25 , b =-20  e c=4

25x²-20x+4=0

x'=x''=[20+√(400-400)]/50=20/50=2/5

g) 4x² - x + 1 = x + 3x²    ==>a=1 , b=-2  e  c=1

x²-2x+1=0

x'=x''=[2+√(4-4)]/2=2/2=1

h) 3x² + 5x = -x – 9 + 2x²   a=1  ,b =6 e c=9

x²+6x +9=0

x'=x''=[-6+√(36-36)]/2=-6/2=-3

i) 4 + x ( x - 4) = x   ==>4+x²-4x=x  ==>a=1 , b=-5x e c=4

x²-5x+4=0

x'=[5+√(25-16)]/2=(5+3)/2=4

x''=[5-√(25-16)]/2=(5-3)/2=1

j) x ( x + 3) – 40 = 0 ==>x²+3x-40=0 ==>a=1 , b=3  e c=-40

x'=[-3+√(9+160)]/2=(-3+13)/2=5

x''=[-3-√(9+160)]/2=(-3-13)/2=-8