Задание: Разложите на множители квадратный трёхчлен

1)

2)

3)

4)

1) = - 5 (х + 0,2) (х - 1)

D = 16 - 4 (-5) = 36

х1 = (-4+6) / (-10) = - 0,2

х2 = (-4 - 6) / (-10) = 1

2) = - 21 (х + 2/7) (х - 2/6) = - 3*7 (х + 2/7) (х - 2/6) =

= - (7 х + 2) (3 х - 1)

D = 1 - 4 (-21) * 2 = 169

√ D = √ 169 = 13

х1 = (-1 + 13) / (-42) = - 12/42 = - 2/7

х2 = (-1 - 13) / (-42) = 14/42 = 2/6

3) = - 12 (х - 1/3) (х - 1/4) = - (3 х - 1) (4 х - 1)

D = 49 - 4 (-12) (-1) = 49 - 48 = 1

х1 = (-7+1) / (-24) = 6/24 = 1/4

х2 = (-7-1) / (-24) = 8 / 24 = 1/3

4) = 27 (х - 1/3) (х + 1/9) = 3*9 * (х - 1/3) (х + 1/9) =

= (3 х - 1) (9 х + 1)

D = 36 - 4*27 * (-1) = 36 + 108 = 144

х1 = (6+12) / 54 = 18/54 = 1/3

х2 = (6-12) / 54 = - 6 / 54 = - 1/9