a) 3x² - 2x - 1 = 0
a = 3 ; b = -2 ; c = -1
Δ = b² - 4ac = ( -2 )² - 4 · 3 · ( -1 ) = 4 + 12 = 16 = 4²
x₁₂ = ( -b ± √Δ ) / 2a
x₁ = ( 2 + 4 ) / 6 = 6 / 6 = 1
x₂ = ( 2 - 4 ) / 6 = -2 / 6 = - 1 / 3
b) 2x² - 3x - 5 = 0
a = 2 ; b = -3 ; c = -5
Δ = b² - 4ac = ( -3 )² - 4 · 2 · ( -5 ) = 9 + 40 = 49 = 7²
x₁₂ = ( -b ± √Δ ) / 2a
x₁ = ( 3 + 7 ) / 4 = 10 / 4 = 5 / 2
x₂ = ( 3 - 7 ) / 4 = -4 / 4 = -1
c) x² - 6x + 8 = 0
a = 1 ; b = -6 ; c = 8
Δ = b² - 4ac = ( -6 )² - 4 · 1 · 8 = 36 - 32 = 4 = 2²
x₁₂ = ( -b ± √Δ ) / 2a
x₁ = ( 6 + 2 ) / 2 = 8 / 2 = 4
x₂ = ( 6 - 2 ) / 2 = 4 / 2 = 2