Question

Rezolvați ecuațiile :
a) x²+2x+6=0
b) x²-x+4=0

Answer 1

a) x² + 2x + 6 = 0

Δ =b²-4ac=4-24=-20

x₁ = (-b+√Δ)/2a=(-2+√-20)/2=1+i√5

x₂ = (-b-√Δ)/2a=(-2-√-20)/2=1-i√5

b)

x²-x+4=0

Δ =b²-4ac=1-16=-15

x₁ = (-b+√Δ)/2a=(-1+√-)/2=(1+i√15)/2

x₂ = (-b-√Δ)/2a=(-1-√-15)/2=(1-i√15)/2

Answer 2

a) a = 1, b = 2, c = 6 Delta = b² -4ac = 4 -4*1*6 = 4-24 = -20 <0 => x nu apartine lui lR Ecuatia data nu are radacini in lR, dar are in multimea nr complexe. x1 = (-b + i√(-delta))/2a = (2+2√5 i)/2 = 2(1+i√5)/2 = 1+i√5 x2 = 1-i√5 b) a = 1, b=-1, c = 4 Delta = b²-4ac = 1-4*1*4 = 1-16 = -15 < 0 => x nu apartine lui lR Ecuatia data nu are radacini in lR, dar are in multimea nr complexe. => x1 = (1+i√15)/2 x2 = (1-i√15)/2