Differential EquationMedium
Question
If f(x) is a polynomial of degree four with leading coefficient unity such that f(1) = 1, f(2) = 4, f(3) = 9, then (f(5) + f(-1)) is-
Options
A.170
B.85
C.43
D.0
Solution
f(x) - x2 = (x - 1) (x - 2) (x - 3) (x - α)
f(5) = 25 + 4.3.2 (5 - α)
f(-1) = 1 + 2.3.4(1 + α)
f(5) + f(-1) = 26 + 24.6 = 170
f(5) = 25 + 4.3.2 (5 - α)
f(-1) = 1 + 2.3.4(1 + α)
f(5) + f(-1) = 26 + 24.6 = 170
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