Question

Resolva as equações em R:
a) x^2-5=0
b) x^2-6x=0
c) 2x^2-5x+3=0
d) -x^2+3x-2=0

Answer 1

a) x² -5=0

x² = 5

x = ± √5

x' = √5 e x'' = -√5

b) x² -6x=0

x(x-6) = 0

x' = 0

x'' -6 = 0

x'' = 6

c) 2x²-5x+3=0

Δ = b² -4ac

Δ (-5)² - 4.2.3

Δ = 25 - 2

Δ = 1

x = -b ± √Δ/2s

x' = 5 + 1 / 4

x' = 6/4

x' = 3/2

x'' = 5 - 1 /4

x'' = 4/4

x'' = 1

d) -x² +3x-2=0

Δ = b² -4ac

Δ (3)² - 4.-1.-2

Δ = 9 - 8

Δ = 1

x = -b ± √Δ/2s

x' = -3 + 1 / -2

x' = -2/-2

x' = 1

x'' = -3 - 1 / -2

x'' = -4/-2

x'' = 2