Let f(x) = (x+1)(x+2)...(x+100) and g(x) = f(x).f''(x) - ( f'(x))^2 . Let n be number of real roots of g(x)=0, then : (a.) n2 (c.) n100

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Please find below the solution to the asked query:

We havefx=x+1x+2.....x+10f'x=x+1x+2...x+9+x+1x+2...x+8x+10+...+x+2.....x+10f'xfx=1x+10+1x+9+....+1x+1=r=110 1x+rf'xfx= r=110 1x+rDifferentiate both sidesf'xfx' =-r=110 1x+r2Nowgx=fxf''x-f'x2=fx2f'xfx'=-fx2r=110 1x+r2gx=0fxf''x-f'x2=0If we represent roots as ai

Hence n=0

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