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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)^15` in powers of x, then the ordered pair (a,b) is equal to
(A)` (28, 315)`
(B)`(-21, 714) `
(C) `(28, 861)`
(D) `(-54, 315)`

A

(28, 315)

B

(-21, 714)

C

(28, 861)

D

(-54, 315)

Text Solution

AI Generated Solution

To solve the problem, we need to find the ordered pair \((a, b)\) such that the coefficients of \(x^2\) and \(x^3\) in the expansion of \((1 + ax + bx^2)(1 - 3x)^{15}\) are both zero. ### Step 1: Expand the expression We start with the expression: \[ (1 + ax + bx^2)(1 - 3x)^{15} \] Using the Binomial Theorem, we can expand \((1 - 3x)^{15}\): ...
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