a)x²- 5x -14=0 Δ=81 √Δ=9 x₁=5-9/2*1 x₁=-4/2 x₁=-2 x₂=5+9/2 x₂=14/2 x₂=7 postac iloczynowa y= (x+2)(x-7) b)x²+8x+33=0 Δ=-68 rozwiazanie w postaci iloczynowej nie istnieje c)2x²+5x+3=0 Δ=1 √Δ=1 x₁=-5 -1/2*2 x₁=-6/4 x₁=-3/2 x₂=-5 +1/4 x₂=-4/4 x₂=-1 postac iloczynowa y=(x+3/2)(x+1) d)3x²-13x+10=0 Δ=49 √Δ=7 x₁=13-7/2*3 x₁=6/6 x₁=1 x₂=13+7/6 x₂=20/6 x₂=10/3 postac iloczynowa y=(x-1)(x-10/3) e)3x²-x-4 Δ=49 √Δ=7 x₁=1-7/2*3 x₁=-6/6 x₁=-1 x₂=1+7/6 x₂=8/6 x₂=4/3 postac iloczynowa y=(x+1)(x-4/3) f)-6x²+x+2=0 Δ=49 √Δ=7 x₁=-1-7/-12 x₁=-6/-12 x₁=1/6 x₂=-1+7/-12 x₂=6/-12 x₂=-1/6 postac iloczynowa y=(x-1/6)(x+1/6) g)8x²+6x-9=0 Δ=324 √Δ=18 x₁=-6-18/2*8 x₁=-24/16 x₁=3/2 x₂=-6+18/16 x₂=12/16 x₂=3/4 postac iloczynowa y=(x-3/2)(x-3/4) h)-10x²+37x-7=0 Δ=1089 √Δ=33 x₁=-37-33/-20 x₁=-70/-20 x₁=7/2 x₂=-37+33/-20 x₂=-4/-20 x₂=1/5 postac iloczynowa y=(x-7/2)(x-1/5)
a) y=x²-5x-14 Δ=25+56=81 √Δ=9 x₁=5-9/2=-2 x₂=5+9/2=7 y=(x+2)(x-7) b) y=x²+8x+33 Δ=64-132=-68 nie ma postaci iloczynowej,brak miejsc zerowych c) y=2x²+5x+3 Δ=25-24=1 √Δ=1 x₁=-5-1/4=-6/4=-1½ x₂=-5+1/4=-1 y=2(x+1½)(x+1) d) y=3x²-13x+10 Δ=169-120=49 √Δ=7 x₁=13-7/6=1 x₂=13+7/6=3⅓ y=3(x-1)(x-3⅓) e) y=3x²-x-4 Δ=1+48=49 √Δ=7 x₁=1-7/6=-1 x₂=1+7/6=1⅓ y=3(x+1)(x-1⅓) f) y=-6x²+x+2 Δ=1+48=49 √Δ=7 x₁=-1-7/-12=8/12=⅔ x₂=-1+7/-12=-½ y=-6(x-⅔)(x+½) g) y=8x²+6x-9 Δ=36+288=324 √Δ=18 x₁=-6-18/16=-24/16=-1½ x₂=-6+18/16=12/16=¾ y=8(x+1½)(x-¾) h) y=-10x²+37x-7 Δ=1369-280=1089 √Δ=33 x₁=-37-33/-20=7/2=3½ x₂=-37+33/-20=-5/-20=¼ y=-10(x-3½)(x-¼) ;]
