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JEE Class main Answered

Sir pls solve the following.
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Asked by rsudipto | 29 Dec, 2018, 11:49: AM
answered-by-expert Expert Answer
begin mathsize 16px style L e t space u s space c o n s i d e r space a space f u n c t i o n space f left parenthesis x right parenthesis space equals space fraction numerator a subscript 0 space end subscript x to the power of n plus 1 end exponent over denominator n plus 1 end fraction plus space fraction numerator a subscript 1 space x to the power of n over denominator n end fraction plus fraction numerator a subscript 2 space x to the power of n minus 1 end exponent over denominator n minus 1 end fraction space plus..................... plus fraction numerator a subscript n minus 1 end subscript x squared over denominator 2 end fraction plus a subscript n x
h e n c e space f apostrophe left parenthesis x right parenthesis space equals space a subscript 0 x to the power of n space plus space a subscript 1 x to the power of n minus 1 end exponent space plus space a subscript 2 space x to the power of n minus 2 end exponent space plus space.................. plus a subscript n minus 1 end subscript x space plus space a subscript n

w e space h a v e space f left parenthesis 0 right parenthesis space equals space 0 space space a n d space f left parenthesis 1 right parenthesis space equals space fraction numerator a subscript 0 space end subscript over denominator n plus 1 end fraction plus space fraction numerator a subscript 1 space over denominator n end fraction plus fraction numerator a subscript 2 space over denominator n minus 1 end fraction space plus..................... plus a subscript n minus 1 end subscript over 2 plus a subscript n space equals space 0 space space left parenthesis space g i v e n space i n space q u e s t i o n right parenthesis
B y space R o l l e apostrophe s space t h e o r e m space f apostrophe left parenthesis x right parenthesis space equals space a subscript 0 x to the power of n space plus space a subscript 1 x to the power of n minus 1 end exponent space plus space a subscript 2 space x to the power of n minus 2 end exponent space plus space.................. plus a subscript n minus 1 end subscript x space plus space a subscript n space bold italic h bold italic a bold italic s bold space bold italic a bold italic t bold italic l bold italic e bold italic a bold italic s bold italic t bold space bold italic o bold italic n bold italic e bold space bold italic r bold italic o bold italic o bold italic t
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