a) 2x²+7x+3=0 Δ=b²-4ac=49-24=25 √Δ=5 x1=(-b-√Δ)/2a=(-7-5)/4=-12/4=-3 x2=(-b+√Δ)/2a=(-7+5)/4=-2/4=-1/2 odp. x=-3 ∨ x=-1/2 b)4x²-x-5=0 Δ=1+80=81 √Δ=9 x1=(1-9)/8=-8/8=-1 x2=(1+9)/8=10/8=1 1/4 odp. x=-1 ∨ x=1 1/4 c)28x²-4x+1/7=0 Δ=16-16=0 x0= -b/2a=4/56=1/14 odp. x=1/14 d)-x²+6x+1=0 Δ=36+4=40 √Δ=√40=√(4*10)=2√10 x1=(-6-2√10)/-2 = 3+√10 x2=(-6+2√10)/-2=3-√10 odp. x=3+√10 ∨ x=3-√10 e)-3x²+2x-3=0 Δ=4-36=-32 Δ<0 - brak rozwiązania f)6x²-2x-1=0 Δ=4+24=28 √Δ=√28=√(4*7)=2√7 x1=(2-2√7)/12 = (1-√7)/6 x2=(2+2√7)/12=(1+√7)/6 odp. x=(1-√7)/6 ∨ x=(1+√7)/6
a) 2x²+7x+3 = 0 Δ = b²-4ac = 49-24 = 25 √Δ = 5 x₁ = (-b-√Δ)/2a = (-7-5)/4 = -3 x₂ = (-b+√Δ)/2a = (-7+5)/4 = -1/2 b) 4x²-x-5 = 0 Δ = 1+80 = 81 √Δ = 9 x₁ = (1-9)/8 = -1 x₂ = (1+9)/8 = 1¼ c) 28x²-4x+1/7 = 0 Δ = 16-16 = 0 x₀ = -b/2a = 4/56 x₀ = 1/14 d) -x²+6x+1 = 0 I(-1) x²-6x-1 = 0 Δ = 36+4 = 40 √Δ = √40 = 2√10 x₁ = (6-2√10)/2 = 3-√10 x₂ = (6+2√10)/2 = 3+√10 e) -3x²+2x-3 = 0 I*(-1) 3x²-2x+3 = 0 Δ = 4-36 = -32 Δ < 0, brak pierwiastków równania f) 6x²-2x-1 = 0 Δ = 4+24 = 28 √Δ = √(4*7) = 2√7 x₁ = (2-2√7)/12 = (1-√7)/6 x₂ = (2+2√7)/12 = (1+√7)/6
