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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)
(2*X^3+17*X^2+38*X+15)/(2*X+5) = 0
2*X^3+17*X^2+38*X+15 = 0
2*X^3+17*X^2+38*X+15 = 0
{ 1, -1, 3, -3, 5, -5, 15, -15 }
1
X = 1
2*X^3+17*X^2+38*X+15 = 72
1
-1
X = -1
2*X^3+17*X^2+38*X+15 = -8
-1
3
X = 3
2*X^3+17*X^2+38*X+15 = 336
3
-3
X = -3
2*X^3+17*X^2+38*X+15 = 0
-3
X+3
2*X^2+11*X+5
2*X^3+17*X^2+38*X+15
X+3
-2*X^3-6*X^2
11*X^2+38*X+15
-11*X^2-33*X
5*X+15
-5*X-15
0
2*X^2+11*X+5 = 0
DELTA = 11^2-(2*4*5)
DELTA = 81
DELTA > 0
X = (81^(1/2)-11)/(2*2) or X = (-81^(1/2)-11)/(2*2)
X = -1/2 or X = -5
X in { -5, -1/2, -3}
(X+5)*(X+1/2)*(X+3) = 0
((X+5)*(X+1/2)*(X+3))/(2*X+5) = 0
( X+1/2 )
X+1/2 = 0 // - 1/2
X = -1/2
( X+3 )
X+3 = 0 // - 3
X = -3
( X+5 )
X+5 = 0 // - 5
X = -5
X in { -1/2, -3, -5 }
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