1)X^3- 2x+ ax -2 X1 = -1 x2=? x3=? a=? 2) x^3- 4x +ax+ b x1= 1 x2= 2 x3 =? a=? b=?

Question

1)X^3- 2x+ ax -2
X1 = -1
x2=?
x3=?
a=?

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

Answer 1

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