1. 4x²-3x=0 x(4x-3) = 0 4x-3 =0 lub x=0 4x-3=0 4x= 3 x= 3/4 2. 3x²+2x=0 x(3x+2) =0 3x+2=0 lub x=0 3x=-2 x= -2/3 3. 7x-x²=0 x(7-x) = 0 7-x = 0 lub x=0 x= 7 4. 2x²=x 2x² -x = 0 x(2x -1)= 2x-1 = 0 lub x=0 2x=1 x= 1/2 5. 8x=4x² 8x-4x² =0 4x(2-x)=0 2-x=0 lub 4x=0 x=2 lub x=o 6. 4x²-9=0 (2x-3) (2x+3)=0 2x-3 = 0 lub 2x+3 =0 2x=3 2x=-3 x= 3/2 =1 ½ lub x=-3/2 = - 1 ½ 7. 16x²-25=0 (4x-5)(4x+5) =0 4x-5 =0 lub 4x+5 =0 4x=5 4x=-5 x= 5/4 = 1 ¼ lub x=-5/5 = -1 ¼ 8. 4-100x²=0 (2-10x)(2+10x)=0 2-10x = 0 lub 2+10x= 0 10x=2 lub 10x =-2 x= 2/10=1/5 lub x= -1/5 9. 9x²=1 9x² -1 = 0 (3x-1)(3x+1)=0 3x-1 =0 lub 3x+1 = 0 3x= 1 3x = -1 x= ½ lub x= - ½ 10. 4x²-121=0 (2x-11) (2x+11) = 0 2x-11 =0 lub 2x+11 = 0 2x =11 2x= -11 x= 11/2 = 5 ½ lub x=-11/2 = - 5 ½ 11. x²+6x+9=0 Δ= b² - 4ac = 6² - 4*1*9 = 36 -36 =0 x₀ = -b/2a =-6/2 =-3 12. x²-10x+25=0 Δ= b² - 4ac = (-10)² - 4*1*25 = 100 -100 =0 x₀ = -b/2a =10/2 = 5 13. x²-4x+7=0 Δ= b² - 4ac = (-4)² - 4*1*7 =16 – 28 = 0 nie ma rozwiązań 14. x²-4x+1=0 Δ= b² - 4ac = (-4)² - 4*1*1 = 14 -4 = 12 √Δ = √12 =√4*3 = 2√2 = 2*1,73 ≈3,46 x₁ = (-b-√Δ)/2a = (4-3,46)/2 = 0,54/2 =0,27 ≈0,3 x₂ = (-b+√Δ)/2a = (4+3,46)/2 = 7,46/2 =3,73 ≈3,7 15. 2x²-9x-35=0 Δ= b² - 4ac = (-9)² - 4*2*(-35) =81 +280=361 √Δ = √361 =19 x₁ = (-b-√Δ)/2a = (9-19/4 = -10/4 = -2 ½ x₂ = (-b+√Δ)/2a = (9+19/4 = 28/4 = 7
