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If (1+a x+b x^2)=a0+a1x+a2x^2++a8x^8,w h...

If `(1+a x+b x^2)=a_0+a_1x+a_2x^2++a_8x^8,w h e r ea ,b ,a_0, a_1, ,a_8 in R` such that `a_0+a_1+a_2!=0a n d|a_0a_1a_2a_1a_2a_0a_2a_0a_1|=0,` then the value of `5a/b` is _______.

A

even

B

odd and of the form `3n`

C

odd and of the form `(3n-1)`

D

odd and of the form `(3n+1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` Putting `x=1` and `-1` and adding
`a_(0)+a_(2)+…+a_(50)=(3^(25)+1)/(2)`
`=((1+2)^(25)+1)/(2)`
`=("^(25)C_(0)+^(25)C_(1)*2+^(25)C_(2)*2^(2)+^(25)C_(25)*2^(25)+1)/(2)`
`=(2[1+^(25)C_(1)+^(25)C_(2)*2+...+^(25)C_(25)*2^(24)])/(2)`
`=2[13+^(25)C_(2)+...+^(25)C_(25)*2^(23)]`
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