a)49x kwadrat + 140x + 100 = 0 delta=19600-19600=0 x=1 42/98 b)x kwadrat + 6x + 9 = (2x - 1)kwadrat -3 x kwadrat + 10x + 8 = 0 delta = 100+96 = 196 pierwiastek z delty = 14 x = 4 lub x = -2/3 c)3x kwadrat + 2x + 1 = 3x + 4x kwadrat - 3 -x kwadrat - x + 4 = 0 delta = 17 pierwiastek z delty = pierwiastek z 17 x = 1 / pierwiastek z 17 / -2 lub x = 1+pierwiastek z 17/-2 d)4 - 1/4 x kwadrat - 3x = x kwadrat + 2x + 9 -1 1/4 x kwadrat - 5x - 5 = 0 delta = 25 - 25 = 0 x = 2 Mam nadzieję, że nie popełniłam żadnego błędu ;)
a) 49x² + 140x + 100 = 0 Δ= b² - 4ac =(1 40) - 4*49*100 = 19600 – 19600 = 0 x₀ = -b)/2a = -140/98 = - 1i 42/98= - 1 i 6/14 b) x² + 6x + 9 = (2x - 1)² x² + 6x + 9 = 4x² - 4x + 1 x² + 6x + 9 - 4x² + 4x – 1 = 0 -3x² + 10x +8 = 0 Δ= b² - 4ac =10² - 4*(-3)*8 = 100 + 96=196 √Δ = √196 = 14 x₁ = (-b-√Δ)/2a =(10-14)/-6 = -4/-6 = 2/3 x₂ = (-b+√Δ)/2a =(10+14)/-6 = 24/-6 = -4 c) 3x² + 2x + 1 = 3x + 4x² - 3 3x² + 2x + 1 - 3x - 4x²+ 3 =0 -x² -x +4 = 0 Δ= b² - 4ac = (-1)² - 4*(-1)*4 = 1 = 1+16 =17 √Δ = √17 x₁ = (-b-√Δ)/2a =(1 -√17)/-2 x₂ = (-b+√Δ)/2a =(1 +√17)/-2 d) 4 - 1/4 x² - 3x = x² + 2x + 9 /* 4 16 -x² -12x -4x² -8x -36 = 0 -5x² -20x -20 = 0 : (-5) x² +4x +4 =0 Δ= b² - 4ac =4² - 4*1*4 = 16 - 16=0 x₀ = -b/2a = -4/2 = -2
