Home Competitions CGMO 2015 Problem 2
Let a ∈ ( 0 , 1 ) a\in(0,1) a ∈ ( 0 , 1 ) f ( x ) = a x 3 + ( 1 − 4 a ) x 2 + ( 5 a − 1 ) x − 5 a + 3 f(x)=ax^3+(1-4a)x^2+(5a-1)x-5a+3 f ( x ) = a x 3 + ( 1 − 4 a ) x 2 + ( 5 a − 1 ) x − 5 a + 3 g ( x ) = ( 1 − a ) x 3 − x 2 + ( 2 − a ) x − 3 a − 1 g(x)=(1-a)x^3-x^2+(2-a)x-3a-1 g ( x ) = ( 1 − a ) x 3 − x 2 + ( 2 − a ) x − 3 a − 1 x x x ∣ f ( x ) ∣ |f(x)| ∣ f ( x ) ∣ ∣ g ( x ) ∣ |g(x)| ∣ g ( x ) ∣ a + 1 a+1 a + 1
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