Question

${x}^{2} - 2x + 4 = 0$
cum se rezolva in multimea nr complexe ? rezolvare completa va rog

Answer 1

x² - 2x + 4 = 0 
Δ = b² - 4ac = (-2)² - 4×4×1 = 4 - 16 = -12 

In cazul in care discriminantul (delta  Δ) este < 0 , ecuatia are 2 radacini
complex conjugate  date de  formula    x₁,₂ = (-b +- i√Δ) / 2a 

x₁ = (2 + i√-12) / 2 

x₂ = (2 - i√-12) / 2 

Answer 2

x1,2=(2+-√(4-16))/2=(2+-√(-12))/2
tinem cont ca
√(-12)=√(12*(-1))=√(12i²)=√i²*√12=i√12=2√3 *i

atunci x1,2=(2+-2√3 8i)/2=1+-i√3

verificare , Viete
x1+x2=2=-(-2)
x1x2=1+3=4
bine rezolvat