(4x^3+2x^2+50)/(2x+5)

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Solution for (4x^3+2x^2+50)/(2x+5) equation: 


D( x )

2*x+5 = 0

2*x+5 = 0

2*x+5 = 0

2*x+5 = 0 // - 5

2*x = -5 // : 2

x = -5/2

x in (-oo:-5/2) U (-5/2:+oo)

(4*x^3+2*x^2+50)/(2*x+5) = 0

4*x^3+2*x^2+50 = 0

2*(2*x^3+x^2+25) = 0

2*x^3+x^2+25 = 0

{ 1, -1, 5, -5, 25, -25 }

1

x = 1

2*x^3+x^2+25 = 28

1

-1

x = -1

2*x^3+x^2+25 = 24

-1

5

x = 5

2*x^3+x^2+25 = 300

5

-5

x = -5

2*x^3+x^2+25 = -200

-5

25

x = 25

2*x^3+x^2+25 = 31900

25

-25

x = -25

2*x^3+x^2+25 = -30600

-25

{ 1/2, -1/2, -1/2, 1/2, 5/2, -5/2, -5/2, 5/2, 25/2, -25/2, -25/2, 25/2 }

1/2

x

1/2

2*x^3+x^2+25 = 25.5

1/2

-1/2

x

-1/2

2*x^3+x^2+25 = 25

-1/2

-1/2

x

-1/2

2*x^3+x^2+25 = 25

-1/2

1/2

x

1/2

2*x^3+x^2+25 = 25.5

1/2

5/2

x

5/2

2*x^3+x^2+25 = 62.5

5/2

-5/2

x

-5/2

2*x^3+x^2+25 = 0

-5/2

x+5/2

2*x^2-4*x+10

2*x^3+x^2+25

x+5/2

-2*x^3-5*x^2

25-4*x^2

4*x^2+10*x

10*x+25

-10*x-25

0

2*x^2-4*x+10 = 0

DELTA = (-4)^2-(2*4*10)

DELTA = -64

DELTA < 0

x in { -5/2} 

2*(x+5/2) = 0

(2*(x+5/2))/(2*x+5) = 0

x+5/2 = 0 // - 5/2

x = -5/2

x in { -5/2} 

x belongs to the empty set

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