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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)
(10*x^3-(19*x^2)-(2*x)+12)/(2*x-3) = 0
(10*x^3-19*x^2-2*x+12)/(2*x-3) = 0
10*x^3-19*x^2-2*x+12 = 0
10*x^3-19*x^2-2*x+12 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 }
1
x = 1
10*x^3-19*x^2-2*x+12 = 1
1
-1
x = -1
10*x^3-19*x^2-2*x+12 = -15
-1
2
x = 2
10*x^3-19*x^2-2*x+12 = 12
2
-2
x = -2
10*x^3-19*x^2-2*x+12 = -140
-2
3
x = 3
10*x^3-19*x^2-2*x+12 = 105
3
-3
x = -3
10*x^3-19*x^2-2*x+12 = -423
-3
4
x = 4
10*x^3-19*x^2-2*x+12 = 340
4
-4
x = -4
10*x^3-19*x^2-2*x+12 = -924
-4
6
x = 6
10*x^3-19*x^2-2*x+12 = 1476
6
-6
x = -6
10*x^3-19*x^2-2*x+12 = -2820
-6
12
x = 12
10*x^3-19*x^2-2*x+12 = 14532
12
-12
x = -12
10*x^3-19*x^2-2*x+12 = -19980
-12
{ 1/2, -1/2, 1/5, -1/5, 1/10, -1/10, -1/2, 1/2, -1/5, 1/5, -1/10, 1/10, 2/2, -2/2, 2/5, -2/5, 2/10, -2/10, -2/2, 2/2, -2/5, 2/5, -2/10, 2/10, 3/2, -3/2, 3/5, -3/5, 3/10, -3/10, -3/2, 3/2, -3/5, 3/5, -3/10, 3/10, 4/2, -4/2, 4/5, -4/5, 4/10, -4/10, -4/2, 4/2, -4/5, 4/5, -4/10, 4/10, 6/2, -6/2, 6/5, -6/5, 6/10, -6/10, -6/2, 6/2, -6/5, 6/5, -6/10, 6/10, 12/2, -12/2, 12/5, -12/5, 12/10, -12/10, -12/2, 12/2, -12/5, 12/5, -12/10, 12/10 }
1/2
x
1/2
10*x^3-19*x^2-2*x+12 = 7.5
1/2
-1/2
x
-1/2
10*x^3-19*x^2-2*x+12 = 7
-1/2
1/5
x
1/5
10*x^3-19*x^2-2*x+12 = 10.92
1/5
-1/5
x
-1/5
10*x^3-19*x^2-2*x+12 = 11.56
-1/5
1/10
x
1/10
10*x^3-19*x^2-2*x+12 = 11.62
1/10
-1/10
x
-1/10
10*x^3-19*x^2-2*x+12 = 12
-1/10
-1/2
x
-1/2
10*x^3-19*x^2-2*x+12 = 7
-1/2
1/2
x
1/2
10*x^3-19*x^2-2*x+12 = 7.5
1/2
-1/5
x
-1/5
10*x^3-19*x^2-2*x+12 = 11.56
-1/5
1/5
x
1/5
10*x^3-19*x^2-2*x+12 = 10.92
1/5
-1/10
x
-1/10
10*x^3-19*x^2-2*x+12 = 12
-1/10
1/10
x
1/10
10*x^3-19*x^2-2*x+12 = 11.62
1/10
2/2
x
2/2
10*x^3-19*x^2-2*x+12 = 1
2/2
-2/2
x
-2/2
10*x^3-19*x^2-2*x+12 = -15
-2/2
2/5
x
2/5
10*x^3-19*x^2-2*x+12 = 8.8
2/5
-2/5
x
-2/5
10*x^3-19*x^2-2*x+12 = 9.12
-2/5
2/10
x
2/10
10*x^3-19*x^2-2*x+12 = 10.92
2/10
-2/10
x
-2/10
10*x^3-19*x^2-2*x+12 = 11.56
-2/10
-2/2
x
-2/2
10*x^3-19*x^2-2*x+12 = -15
-2/2
2/2
x
2/2
10*x^3-19*x^2-2*x+12 = 1
2/2
-2/5
x
-2/5
10*x^3-19*x^2-2*x+12 = 9.12
-2/5
2/5
x
2/5
10*x^3-19*x^2-2*x+12 = 8.8
2/5
-2/10
x
-2/10
10*x^3-19*x^2-2*x+12 = 11.56
-2/10
2/10
x
2/10
10*x^3-19*x^2-2*x+12 = 10.92
2/10
3/2
x
3/2
10*x^3-19*x^2-2*x+12 = 0
3/2
x-3/2
10*x^2-4*x-8
10*x^3-19*x^2-2*x+12
x-3/2
15*x^2-10*x^3
12-4*x^2-2*x
4*x^2-6*x
12-8*x
8*x-12
0
10*x^2-4*x-8 = 0
DELTA = (-4)^2-(-8*4*10)
DELTA = 336
DELTA > 0
x = (336^(1/2)+4)/(2*10) or x = (4-336^(1/2))/(2*10)
x = (4*21^(1/2)+4)/20 or x = (4-4*21^(1/2))/20
x in { (4-4*21^(1/2))/20, (4*21^(1/2)+4)/20, 3/2}
(x-((4-4*21^(1/2))/20))*(x-((4*21^(1/2)+4)/20))*(x-3/2) = 0
((x-((4-4*21^(1/2))/20))*(x-((4*21^(1/2)+4)/20))*(x-3/2))/(2*x-3) = 0
( x-((4*21^(1/2)+4)/20) )
x-((4*21^(1/2)+4)/20) = 0 // + (4*21^(1/2)+4)/20
x = (4*21^(1/2)+4)/20
( x-((4-4*21^(1/2))/20) )
x-((4-4*21^(1/2))/20) = 0 // + (4-4*21^(1/2))/20
x = (4-4*21^(1/2))/20
( x-3/2 )
x-3/2 = 0 // + 3/2
x = 3/2
x in { 3/2}
x in { (4*21^(1/2)+4)/20, (4-4*21^(1/2))/20 }
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