(2x3+x2-13x+6)/x+3

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Solution for (2x3+x2-13x+6)/x+3 equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

(2*x^3+x^2-(13*x)+6)/x+3 = 0

(2*x^3+x^2-13*x+6)/x+3 = 0

(2*x^3+x^2-13*x+6)/x+(3*x)/x = 0

2*x^3+x^2-13*x+3*x+6 = 0

2*x^3+x^2-10*x+6 = 0

2*x^3+x^2-10*x+6 = 0

2*x^3+x^2-10*x+6 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6 }

1

x = 1

2*x^3+x^2-10*x+6 = -1

1

-1

x = -1

2*x^3+x^2-10*x+6 = 15

-1

2

x = 2

2*x^3+x^2-10*x+6 = 6

2

-2

x = -2

2*x^3+x^2-10*x+6 = 14

-2

3

x = 3

2*x^3+x^2-10*x+6 = 39

3

-3

x = -3

2*x^3+x^2-10*x+6 = -9

-3

6

x = 6

2*x^3+x^2-10*x+6 = 414

6

-6

x = -6

2*x^3+x^2-10*x+6 = -330

-6

{ 1/2, -1/2, -1/2, 1/2, 2/2, -2/2, -2/2, 2/2, 3/2, -3/2, -3/2, 3/2, 6/2, -6/2, -6/2, 6/2 }

1/2

x

1/2

2*x^3+x^2-10*x+6 = 1.5

1/2

-1/2

x

-1/2

2*x^3+x^2-10*x+6 = 11

-1/2

-1/2

x

-1/2

2*x^3+x^2-10*x+6 = 11

-1/2

1/2

x

1/2

2*x^3+x^2-10*x+6 = 1.5

1/2

2/2

x

2/2

2*x^3+x^2-10*x+6 = -1

2/2

-2/2

x

-2/2

2*x^3+x^2-10*x+6 = 15

-2/2

-2/2

x

-2/2

2*x^3+x^2-10*x+6 = 15

-2/2

2/2

x

2/2

2*x^3+x^2-10*x+6 = -1

2/2

3/2

x

3/2

2*x^3+x^2-10*x+6 = 0

3/2

x-3/2

2*x^2+4*x-4

2*x^3+x^2-10*x+6

x-3/2

3*x^2-2*x^3

4*x^2-10*x+6

6*x-4*x^2

6-4*x

4*x-6

0

2*x^2+4*x-4 = 0

DELTA = 4^2-(-4*2*4)

DELTA = 48

DELTA > 0

x = (48^(1/2)-4)/(2*2) or x = (-48^(1/2)-4)/(2*2)

x = (4*3^(1/2)-4)/4 or x = (-4*3^(1/2)-4)/4

x in { (-4*3^(1/2)-4)/4, (4*3^(1/2)-4)/4, 3/2} 

(x-((-4*3^(1/2)-4)/4))*(x-((4*3^(1/2)-4)/4))*(x-3/2) = 0

((x-((-4*3^(1/2)-4)/4))*(x-((4*3^(1/2)-4)/4))*(x-3/2))/x = 0

((x-((-4*3^(1/2)-4)/4))*(x-((4*3^(1/2)-4)/4))*(x-3/2))/x = 0 // * x

(x-((-4*3^(1/2)-4)/4))*(x-((4*3^(1/2)-4)/4))*(x-3/2) = 0

( x-((-4*3^(1/2)-4)/4) )

x-((-4*3^(1/2)-4)/4) = 0 // + (-4*3^(1/2)-4)/4

x = (-4*3^(1/2)-4)/4

( x-((4*3^(1/2)-4)/4) )

x-((4*3^(1/2)-4)/4) = 0 // + (4*3^(1/2)-4)/4

x = (4*3^(1/2)-4)/4

( x-3/2 )

x-3/2 = 0 // + 3/2

x = 3/2

x in { (-4*3^(1/2)-4)/4, (4*3^(1/2)-4)/4, 3/2 }

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