Тема: формулы корней квадратных уравнений.
Задание:
1) а) 3х^-8x+5=0
б) 4x^+x+67=0
2) a) 5x^+26x-24=0
б) 4x^-12x+9=0
3) a) -x^+26x-25=0
б) -5x^-9x+2=0
4) a) x^=4x+96
б) 2x^-2=3x

2

Ответы и объяснения

2014-02-09T14:36:19+04:00
1) а) 3х^-8x+5=0
D=64-60=4 (2)
x1=8+2/6=10/6=5/3
x2=8-2/6=2/3

б) 4x^+x+67=0
D=1-4*4*67 D<0, корней нет

2) a) 5x^+26x-24=0
D=676-4*(-24)*5=1156 (34)
x1=34-26/10=0.8
x1=34+26/10=6

б) 4x^-12x+9=0
D=144-144=0
x=-12/8=-1.5

3) a) -x^+26x-25=0
D=676-100=576 (24)
x1=-26+24/-2=1
x2=-26-24/-2=25

б) -5x^-9x+2=0
D=81+40=121 (11)
x1=9+11/-10=-2
x2=9-11/-10=0.2

4) a) x^=4x+96
x^-4x-96=0
D=16+384=400 (20)
x1=4+20/2=24/2=12
x2=4-20/2=-8

б) 2x^-2=3x
2x^-2-3x=0
D=9+16=25 (5)
x1=3+5/4=2
x2=3-5/4=-0.5
2014-02-09T14:47:40+04:00
1. а) 3х^2 - 8x + 5=0
D = 64 - 60 = 4
x1 = (8 + 2)/6 = 10/6
x2 = (8-2)/6 = 1
б) 4x^2 + x + 67 = 0
D = 1 - 1072 = -1071
не имеет решения
2. а) 5x^2 + 26x - 24 = 0
D = 676 + 480 = 1156
x1 = (-26 + 34)/10 = 0.8
x2 = (-26 - 34)/10 = -6
б) 4x^2 - 12x +9=0
D= 144 - 144 = 0
x1 = x2 = 12/8 
3. a) -x^2 -26x - 25 = 0
x^2 + 26 +25=0
D=676-100=576
x1 = (-26 + 24)/2 = -1
x2 = (-26 - 24)/2 = -25
б) -5x^2 - 9x + 2=0
5x^2 + 9x - 2 =0
D=81 +40 = 121
x1 = (-9 + 11)/10 = 0.2
x2 = (-9-11)/10 = -2
4. а) x^2 - 4x - 96 = 0
D = 16 + 384 = 400
x1 = (4+ 20) / 2 = 12
x2 = (4-20)/2 = -8
б) 2x^2 - 3x - 2 =0
D= 9 + 16 = 25
x1 = (3+5)/4 = 2
x2=(3-5)/4 = -0.5