Równania kwadratowe.
1)(x-1)(x+8)=0
2)x²-3=0
3)x²+4=0
4)x²+6x=0
5)(x-1)(x+3)=(x+4)(x-4)
6)(x-4)(x+8)=((x-4)(3x-2)
7)x²+7x+6=0
8)-x²+6x+2=0
9)x²-4x+10=0
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1. (x-1)(x=8)=0
x-1 = 0 lub x+8=0
x= 1 lub x= -8
2. x²-3=0
Δ=0²-4×1×(-3)= 12 > 0
√Δ≈3,46
x1= -3,46/2 = - 1,73
x2= 3,46/2 = 1,73
3. x²+4=0
Δ=0²-4×1×4= -16 <0 brak pierwiastków.
4. x²+6x=0
Δ=6²-4×1×0= 36 >0
√Δ= 6
x1= -6-6/2 = -12/2 = -6
x2= -6+6/2 = 0
5.(x-1)(x+3)=(x+4)(x-4)
x²+3x-x-3=x²-4x+4x-16
x²-x²+3x-x+4x-4x-3+16=0
2x+13=0
Δ= (2)²-4×0×13= 4 >0
√Δ=2
x1=1-2/0= -1/0
x2=1+2/0=3/0
6.(x-4)(x+8)=(x-4)(3x-2)
x²+8x-4x-32=3x²-2x-12x+8
x²-3x²+8x-4x+2x+12x-32-8=0
-2x²+16x-40=0
Δ=16²-4×(-2)×(-40)= 256-320= -64 <0 brak rozwiązań
7. x²+7x+6=0
Δ=7²-4×1×6= 49-24=25 >0
√Δ=5
x1=-7-5/2= -12/2= -6
x2=-7+5/2= 2/2 =1
8. -x²+6x+2=0
Δ=6²-4×(-1)×2= 36+8=44 >0
√Δ=6,63
x1=-6-6,63/-2= -12,63/-2 = 6,315
x2=-6+6,63/-2= 0,63/-2= -0,315
9. x²-4x+10=0
Δ=(-4)²-4×1×10=16-40 = -24 <0 brak pierwiastków.