a) R=x² - 4x + 3 = 0

a = 1, b = - 4, c = 3

∆ = b² - 4ac

∆ = ( - 4 )² - 4 • 1 • 3

∆ = 16 - 12

∆ = 4

x = - b ± √∆ / 2a

x = - ( - 4 ) ± √4 / 2 • 1

x = 4 ± 2 / 2

x' = 4 + 2/2

x' = 6/2

x' = 3

x" = 4 - 2/2

x" = 2/2

x" = 1

S = { 1, 3 }

b) R=2x² - 11x +5 = 0

Δ=b²-4ac

Δ=(-11)²-4(2)(5)

Δ=121-40

Δ=81

x=-b+-√Δ/2a

x=-(-11)+-√81/2(2)

x=11+-9/4

x'=11+9/4

x'=20/4

x'=5

x''=11-9/4

x''=2/4

x''=0,5

c) R=f ( x ) = 0

f ( x ) = x² - 4x + 4

0 = x² - 4x + 4

a = 1, b = - 4, c = 4

∆ = b² - 4ac

∆ = ( - 4 )² - 4 • 1 • 4

∆ = 16 - 16

∆ = 0

x = - b/2a

x = - ( - 4 )/2 • 1

x = 4/2

x' = 2

x' = x" = 2

R = A raiz da função é 2

d) R=3x²-9x+6=0

Δ=b²-4.a.c

Δ=-9²-4.3.6

Δ=81-72

Δ=9

x=-b+ou-√Δ / 2a

x=-(-9)+ou-√9 / 2x3

x=9+ou-3 / 6

x1=9+3 / 6 

x1=12 / 6

x1=2

x2=9-3 / 6

x2=6 / 6

x2=1