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If the coefficients of x^(2) and x^(3)ar...

If the coefficients of `x^(2)` and `x^(3)`are both zero, in the expansion of the expression `(1 + ax + bx^(2)) (1 - 3x)` in powers of x, then the ordered pair (a,b) is equal to

A

`(-21, 714)`

B

(-54, 315)

C

(28, 861)

D

(28, 315)

Text Solution

Verified by Experts

The correct Answer is:
D
Given expression is `(1+ax + bx^(2))(1-3x)^(15)`
Coff. Of `x^(2)=0`
Coff of `x^(3)=0`
Coff of `x^(2) = ""^(15)C_(2) xx 9 + b-""^(15)C_(1) xx 3b + ""^(15)C_(2) xx 9a`
`rArr 945a - 456 = 12285` (given)………….(2)
On solving (1) and (2) we get
a=28, b=315
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