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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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Clearly , let
f'(x) = kx^(2)(x - 2) (1 + x^(2)), k ne 0 = k (x^(5) - 2x^(4) + x^(3) - 2x^(2))`
`rArr f(x) = `(kx^(3))/(60) (10x^(3) - 24x^(2) + 15x - 40) therefore `(3f(2))/(f(1)) = (3 xx8(-26))/(-39) = 16`
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