Тема: формулы корней квадратных уравнений.

Задание:

1) а) 3 х^-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

1) а) 3 х^-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

1. а) 3 х^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