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Let f(x) be a polynomial of degree 6 di...

Let f(x) be a polynomial of degree 6 divisible by `x^(3)` and having a point of extremum at x = 2 . If f'(x) is divisible by `1 + x^(2)`, then find the value of `(3f(2))/(f(1))`.

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The correct Answer is:
16
Clearly , let
`f.(x) = kx^(2) (x-2) (1+x^2 ), k ne 0 = k (x^(5) - 2x^(4) + x^(3) - 2x^(2))`
`implies f(x) = (kx^(3))/(60) ( 10x^(3) - 24x^(2) + 15x - 40) :. (3f(2))/(f(1))=(3xx 8(-26))/(-39) =16 `
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