If f x is a polynomial of degree four with the leading coefficient one satisfying f 1 = 1 , f ( 2 ) = 2 and f ( 3 ) = 3 , then f - 1 + f 5 f 0 + f 4 (where · represents the greatest integer function) is equal to

Step-by-step solution

The roots of f x − x = 0 are 1 , 2 and 3 . So, we get, f x − x = x − 1 x − 2 x − 3 x − a For x = - 1 , we get, f − 1 + 1 = − 2 − 3 − 4 − 1 − a = 24 1 + a For x = 5 , we get, f 5 − 5 = 4 · 3 · 2 5 − a = 24 5 − a f - 1 + f 5 = 23 + 24 a + 125 - 24 a = 148 For x = 0 , we get, f 0 - 0 = - 1 - 2 - 3 - a = 6 a For x = 4 , we get, f 4 - 4 = 3 · 2 · 1 · 4 - a = 24 - 6 a f 0 + f 4 = 28 f - 1 + f 5 f 0 + f 4 = 1