a) x²-8x+16=0 Δ=(-8)²-4*1*16 Δ=64-64 Δ=0 x0=8/2*1=4 y=(x-4)² b) x²-x+1/4=0 Δ=(-1)²-4*1*1/4 Δ=1-1 Δ=0 x0=1/2=½ y=(x-½)² c) x²+2x-8=0 Δ=2²-4*1*(-8) Δ=4+32 Δ=36 x1=(-2-6)/2=-4 x2=(-2+6)/2=2 y=(x+4)(x-2) d) 3x²-4x+1=0 Δ=(-4)²-4*3*1 Δ=16-12 Δ=4 x1=(4-2)/6=⅓ x2=(4+2)/6=1 y=3(x-⅓)(x-1) e) x²-4x+25=0 Δ=(-4)²-4*1*25 Δ=16-100 Δ=-84 brak rozwiazania f) 2x²-3x+12,25=0 Δ=(-3)²-4*2*12,25 Δ=9-98 Δ=-89 brak rozwiazania
a) x²-8x+16=0 Δ =b²-4ac Δ= (-8)² -4*1*16 Δ = 64-64 Δ=0 x₀ = -b/2a x₀ = -(-8) / 2*1 x₀ = 8/2 x₀ = 4 b) x²-x+1/4=0 Δ =b²-4ac Δ= (-1)² -4*1*1/4 Δ =1-1 Δ=0 x₀ = -b/2a x₀ = -(-1) / 2*1 x₀ = 1/2 c) x²+2x-8=0 Δ =b²-4ac Δ= (2)² -4*1*(-8) Δ = 4+32 Δ=36 √Δ=√36 √Δ= 6 x₁ = (-b+√Δ) / 2a x₁ = (-2+6) / 2*1 x₁ = -12/2 x₁ = -6 x₂ = (-b-√Δ) / 2a x₂ = (-2-6) / 2*1 x₂ = (-8) / 2 x₂ = -4 d) 3x²-4x+1=0 Δ =b²-4ac Δ= (-4)² -4*3*1 Δ = 16-12 Δ=4 √Δ=√4 √Δ= 2 x₁ = (-b+√Δ) / 2a x₁ = (4+2) / 2*3 x₁ = 8/6 x₁ = 1 ⅓ x₂ = (-b-√Δ) / 2a x₂ = (4-2) / 2*3 x₂ = 2 / 6 x₂ = ⅓ e) x²-4x+25=0 Δ =b²-4ac Δ= (-4)² -4*1*25 Δ = 16-100 Δ=-84 brak rozwiązania f) 2x²-3x+12,25=0 Δ =b²-4ac Δ= (-3)² -4*2*12,25 Δ = 9-98 Δ=-89 brak rozwiązania
