a) 3x^2-4x+1=0 Δ=b²-4ac Δ=(-4)^2 -4*3*1 Δ=16-12 Δ=4 pierwiastek Δ=2 x1 =( -b-pierwiastek Δ)/ 2a i x2 =( -b+pierwiastek Δ)/ 2a x1 = (4-2)/2*3 i x2 = (4+2)/2*3 x1 = 2/6 i x2 = 6/6 x1 = 1/3 i x2 = 1 b) 25x^2 -10x +1= 0 Δ=b²-4ac Δ = (-10)^2 - 4 * 25 * 1 Δ = 100 - 100 Δ = 0 x0 = -b/2a x0 = 10/2*25 x0 = 10/50 x0 = 1/5 c) x²-3x+10=0 Δ=b²-4ac Δ = (-3)^2 - 4*1*10 Δ = 9 - 40 Δ = -31 <0 - brak rozwiązania d) 5x²+4x-1=0 Δ=b²-4ac Δ = 4^2 - 4* 5* (-1) Δ = 16 +20 Δ = 36 pier Δ = 6 x1 =( -b-pierwiastek Δ)/ 2a i x2 =( -b+pierwiastek Δ)/ 2a x1 = (-4-6)/2*5 i x2 = (-4 + 6) /2*5 x1 = -10/10 i x2 = 2/10 x1 = -1 i x2 = 1/5 e) 4x²-4x+1=0 Δ=b²-4ac Δ = (-4) ^2 - 4 * 4 * 1 Δ = 16-16 Δ = 0 x0 = -b /2a x0 = 4/2*4 x0 = 4/8 x0 = 1/2 f) x²+x+1=0 Δ=b²-4ac Δ = 1^2 - 4 * 1 * 1 Δ = 1 - 4 Δ = -3 <0 - brak rozwiązania
