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2 () 1( ) 1( ) −1 ()
3 2 6 6
α1, α2, α3
x 3 + px 2 + 4 ( )
4() . α1 = α2 )
3( ) p
−3 ( )
0( )
[AMC10A 2010] (
f (x ) = x 3 − ax 2 + bx − 2010
108 ( ) 98 ( ) 88 ( ) a
78 ( ) )
(
f (x ) = x 3 − 18x 2 + 87x + k = 0
k
3 ( ) 2 ( ) 1 ( ) 0()
f (x ) = ax 7 + bx 3 + cx − 5 [AHSME 1982] ( )
)
19 ( ) 17 ( ) f (7) f (−7) = 7 )
pq α3 α2 α1 −17 ( ) −19 ( )
α1 + α2 = 0
15 ( ) q≠0 p≠0 (
12 ( )
x 3 + px 2 + qx + 15 = 0
−12 ( ) −15 ( )
6 x −3 f (x ) = ax 5 + bx 3 + cx (
x2 − 9 f (x)
