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Quadratic Polynomial

26. The funct...

Question

26. The function f(x)=0 has eight distinct solutions and f also satisfy f(4+x)= f(4-x). The sum of all eight solutions of f(x)=0 is

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Solution

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f (x) = 0

f

f (4 + x) = f (4 - x)

f (x) = 0

f

R

f (x + y) = f (x) + f (y) \forall x, y ϵ R

f^{'} (0) = 2

f (4)

f (x)

8

f (x) = f (4 - x)

\forall x ϵ R

f (x)

6

f (x) = 0

A

A

f

f (0) = 2, f^{'} (0) = 3

f^{''} (x) = f (x)

f (x)

f (x) f (\frac{1}{x}) = f (x) + (\frac{1}{x})

f (3) = 28

f (4) =

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