Răspuns:
Explicație pas cu pas:
2x² - 200 = 0 <=> 2x² = 200 I:2 => x² = 100 => x₁,₂ = ±√100 = ±10
x²-9 = 0 => x² = 9 => x₁,₂ = ±√9 = ±3
2x²-50 = 0 => 2x² = 50 I:2 => x² = 25 => x₁,₂ = ±√25 => x₁,₂ = ±5
2x²-8 = 0 => 2x² = 8 I:2 => x² = 4 => x₁,₂ = ±√4 = x₁,₂ = ±2
2x²+5x = 0 <=> x(2x+5) = 0 => x₁ = 0 ; x₂ = -5/2
-4x²+x = 0 <=> x(-4x+1) = 0 => x₁=0 ; x₂ = 1/4
6x²-7 = 0 <=> 6x² = 7 => x² = 7/6 => x₁,₂ = ±√(7/6) = ±(√42)/6
x²+4x+3 = 0 <=> x²+3x+x+3 = 0 <=> x(x+3) + x+3 = 0 <=>
(x+3)(x+1) = 0 => x₁ = -3 ; x₂ = -1
4x²-12x = 0 <=> 4x(x-3) = 0 => x₁ = 0 ; x₂ = 3
x²-x+1 = 0 ; x₁,₂ ∉ R
a = 1 ; b = -1 ; c = 1
Δ = b²-4ac = (-1)²-4·1·1 = 1-4 = -3
√Δ = √(-3) = i√3
x₁,₂ = (-b±√Δ)/2a = (1±i√3)/2 ∈ C
