- #1

utkarshakash

Gold Member

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## Homework Statement

If f(x) is differentiable function satisfying [itex] 6x \displaystyle \int_0^1 f(tx)dt = 2x^3-3x^2+6x+5 [/itex] then select correct options(more than one may be correct)

a)f(x) is symmetric about x=1

b)f(x)=0 has no real roots

c)f(-x)=f(x+1) for all x in R

d) f(x)=1/2 has 2 real and equal roots

## The Attempt at a Solution

From the options it is clear that the function f(x) is to be determined first. Now, if I divide both sides by 6,

[itex] x \displaystyle \int_0^1 f(tx)dt = \int (x^2 - x +1) dx + \frac{5}{6} [/itex]

I have no idea how to take it ahead.