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If be a monic polynomial of degree four and satisfying .
If , find .
Details
Monic polynomial means polynomial whose leading coefficient is 1.
The answer is 5.
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According to the given condition we can write f ( x ) = ( x − a ) ( x − 1 ) ( x − 2 ) ( x − 3 ) + 1 0 x Therefore , f ( 1 2 ) = ( 1 1 ) ( 1 0 ) ( 9 ) ( 1 2 − a ) + 1 2 0 f ( − 8 ) = ( 1 1 ) ( 1 0 ) ( 9 ) ( 8 + a ) − 8 0 f ( 1 2 ) + f ( − 8 ) = ( 1 1 ) ( 1 0 ) ( 9 ) ( 1 2 − a + 8 + a ) + 4 0 f ( 1 2 ) + f ( − 8 ) = ( 1 1 ) ( 1 0 ) ( 9 ) ( 2 0 ) + 4 0 f ( 1 2 ) + f ( − 8 ) = 3 9 6 8 ( 5 ) ω = 5 .