If f ( x ) is a polynomial of degree 4 with leading coefficient one satisfying f ( 1 ) = 1 , f ( 2 ) = 2 , f ( 3 ) = 3 then [ f ( 0 ) + f ( 4 ) f ( − 1 ) + f ( 5 ) ] = ( [.] denotes GIF)

Question

If f ( x ) is a polynomial of degree 4 with leading coefficient one satisfying f ( 1 ) = 1 , f ( 2 ) = 2 , f ( 3 ) = 3 then [ f ( 0 ) + f ( 4 ) f ( − 1 ) + f ( 5 ) ​ ] = ( [.] denotes GIF)

TestHub · Accepted Answer

f ( x ) − x = ( x − 1 ) ( x − 2 ) ( x − 3 ) ( x − α ) ​ f ( − 1 ) = 24 ( 1 + α ) − 1 f ( 0 ) = 6 α f ( 4 ) = 6 ( 4 − α ) + 4 f ( 5 ) = 24 ( 5 − α ) + 5 ​ [ f ( 0 ) + f ( 4 ) f ( − 1 ) + f ( 5 ) ​ ] = [ 28 148 ​ ] = 5

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