1) X^3 - 2x + ax - 2

X1 = - 1

x2=?

x3=?

a=?

2) x^3 - 4x + ax + b

x1 = 1

x2 = 2

x3 = ?

a=?

b=?

1) x^3 - 2x + ax - 2 х1 = - 1 x2=? x3=? a=?

-1^3 - 2 (-1) + a (-1) - 2=0

-1+2-а-2=0

а=-1

x^3 - 2x-x - 2=0

x^3 - 3x - 2=0

(x^3 - 3x - 2) : (х+1) = - x^2+х+2

(х+1) (-x^2+х+2) = 0

-x^2+х+2=0

х2=2 х3=-1

x1=x3=-1

x2=2

2) x^3 - 4x + ax + b x1 = 1 x2 = 2 x3 = ? a=?

x^3 - 4x + ax + b=0

1^3 - 4*1 + a*1 + b=0

a+b=3

2^3 - 4*2 + a*2 + b=0

2a+b=0

b=-2a

a-2a=3

a=-3

b = (-2) * (-3) = 6

x^3 - 4x-3x + 6=0

x^3-7x+6=0

(x-1) (x-2) = x^2-3x+2

(x^3-7x+6) : (x^2-3x+2) = x+3

(x-1) (x-2) (x+3) = 0

(x+3) = 0

x3=-3