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Q.

An equation a0+a1x+a2x2+⋯+a99x99+x100=0 has roots  99C0,99C1,99C2,…,99C99.The value of a99 is equal toThe value of a98 is The value of  99C02+ 99C12+⋯+ 99C992 is equal to

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a

298

b

299

c

-299

d

none of these

e

2198−198C992

f

2198+198C992

g

299−99C49

h

none of these

i

2a98−a992

j

a992−a98

k

a992−2a98

l

none of these

answer is , , .

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Detailed Solution

a0+a1x+a2x2+⋯+a99x99+x100=0 has roots 99C0,99C1,99C2,…,99C99 or  a0+a1x+a2x2+⋯+a99x99+x100 =x−99C0x−99C1x−99C2⋯x−99C99Now, sum of roots is    99C0+99C1+99C2+⋯+99C99=−a99 coefficient of x100 or  a99=−299Also, sum of product of roots taken two at a time isa99 coefficient of x100∴∑∑0≤i
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