(4x^4-17x^2+14x-3)/(2x-3)

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Solution for (4x^4-17x^2+14x-3)/(2x-3) equation: 


D( x )

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0 // + 3

2*x = 3 // : 2

x = 3/2

x in (-oo:3/2) U (3/2:+oo)

(4*x^4-(17*x^2)+14*x-3)/(2*x-3) = 0

(4*x^4-17*x^2+14*x-3)/(2*x-3) = 0

4*x^4-17*x^2+14*x-3 = 0

4*x^4-17*x^2+14*x-3 = 0

{ 1, -1, 3, -3 }

1

x = 1

4*x^4-17*x^2+14*x-3 = -2

1

-1

x = -1

4*x^4-17*x^2+14*x-3 = -30

-1

3

x = 3

4*x^4-17*x^2+14*x-3 = 210

3

-3

x = -3

4*x^4-17*x^2+14*x-3 = 126

-3

{ 1/2, -1/2, 1/4, -1/4, -1/2, 1/2, -1/4, 1/4, 3/2, -3/2, 3/4, -3/4, -3/2, 3/2, -3/4, 3/4 }

1/2

x

1/2

4*x^4-17*x^2+14*x-3 = 0

1/2

x-1/2

4*x^3+2*x^2-16*x+6

4*x^4-17*x^2+14*x-3

x-1/2

2*x^3-4*x^4

2*x^3-17*x^2+14*x-3

x^2-2*x^3

14*x-16*x^2-3

16*x^2-8*x

6*x-3

3-6*x

0

4*x^3+2*x^2-16*x+6 = 0

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

1

x = 1

4*x^3+2*x^2-16*x+6 = -4

1

-1

x = -1

4*x^3+2*x^2-16*x+6 = 20

-1

2

x = 2

4*x^3+2*x^2-16*x+6 = 14

2

-2

x = -2

4*x^3+2*x^2-16*x+6 = 14

-2

3

x = 3

4*x^3+2*x^2-16*x+6 = 84

3

-3

x = -3

4*x^3+2*x^2-16*x+6 = -36

-3

6

x = 6

4*x^3+2*x^2-16*x+6 = 846

6

-6

x = -6

4*x^3+2*x^2-16*x+6 = -690

-6

{ 1/2, -1/2, 1/4, -1/4, -1/2, 1/2, -1/4, 1/4, 2/2, -2/2, 2/4, -2/4, -2/2, 2/2, -2/4, 2/4, 3/2, -3/2, 3/4, -3/4, -3/2, 3/2, -3/4, 3/4, 6/2, -6/2, 6/4, -6/4, -6/2, 6/2, -6/4, 6/4 }

1/2

x

1/2

4*x^3+2*x^2-16*x+6 = -1

1/2

-1/2

x

-1/2

4*x^3+2*x^2-16*x+6 = 14

-1/2

1/4

x

1/4

4*x^3+2*x^2-16*x+6 = 2.1875

1/4

-1/4

x

-1/4

4*x^3+2*x^2-16*x+6 = 10.0625

-1/4

-1/2

x

-1/2

4*x^3+2*x^2-16*x+6 = 14

-1/2

1/2

x

1/2

4*x^3+2*x^2-16*x+6 = -1

1/2

-1/4

x

-1/4

4*x^3+2*x^2-16*x+6 = 10.0625

-1/4

1/4

x

1/4

4*x^3+2*x^2-16*x+6 = 2.1875

1/4

2/2

x

2/2

4*x^3+2*x^2-16*x+6 = -4

2/2

-2/2

x

-2/2

4*x^3+2*x^2-16*x+6 = 20

-2/2

2/4

x

2/4

4*x^3+2*x^2-16*x+6 = -1

2/4

-2/4

x

-2/4

4*x^3+2*x^2-16*x+6 = 14

-2/4

-2/2

x

-2/2

4*x^3+2*x^2-16*x+6 = 20

-2/2

2/2

x

2/2

4*x^3+2*x^2-16*x+6 = -4

2/2

-2/4

x

-2/4

4*x^3+2*x^2-16*x+6 = 14

-2/4

2/4

x

2/4

4*x^3+2*x^2-16*x+6 = -1

2/4

3/2

x

3/2

4*x^3+2*x^2-16*x+6 = 0

3/2

x-3/2

4*x^2+8*x-4

4*x^3+2*x^2-16*x+6

x-3/2

6*x^2-4*x^3

8*x^2-16*x+6

12*x-8*x^2

6-4*x

4*x-6

0

4*x^2+8*x-4 = 0

DELTA = 8^2-(-4*4*4)

DELTA = 128

DELTA > 0

x = (128^(1/2)-8)/(2*4) or x = (-128^(1/2)-8)/(2*4)

x = (8*2^(1/2)-8)/8 or x = (-8*2^(1/2)-8)/8

x in { (-8*2^(1/2)-8)/8, (8*2^(1/2)-8)/8, 1/2, 3/2} 

(x-((-8*2^(1/2)-8)/8))*(x-((8*2^(1/2)-8)/8))*(x-1/2)*(x-3/2) = 0

((x-((-8*2^(1/2)-8)/8))*(x-((8*2^(1/2)-8)/8))*(x-1/2)*(x-3/2))/(2*x-3) = 0

( x-((-8*2^(1/2)-8)/8) )

x-((-8*2^(1/2)-8)/8) = 0 // + (-8*2^(1/2)-8)/8

x = (-8*2^(1/2)-8)/8

( x-((8*2^(1/2)-8)/8) )

x-((8*2^(1/2)-8)/8) = 0 // + (8*2^(1/2)-8)/8

x = (8*2^(1/2)-8)/8

( x-1/2 )

x-1/2 = 0 // + 1/2

x = 1/2

( x-3/2 )

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

x = 3/2

x in { 3/2} 

x in { (-8*2^(1/2)-8)/8, (8*2^(1/2)-8)/8, 1/2 }

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