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If the coefficient of middle terms in $(1+\alpha x)^4$ and $(1-\alpha x)^6$ is same then $\alpha =?$

$\begin{array}{1 1} -\large\frac{5}{3} \\ -\large\frac{3}{10} \\ \large\frac{5}{3} \\ \large\frac{10}{3} \end{array} $

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Toolbox:
  • The midddle term in the expansion of $(1+x)^n$ is $ (\large\frac{n}{2}+1)^{th}$ term
General term in the expansion of $(1+\alpha x)^4 $ is $^4C_r\alpha^r x^r$
General term in the expansion of $(1-\alpha x)^6 $ is $-^6C_r\alpha^r x^r$
The middle term in the expansion of $(1+\alpha x)^4$ is $3^{rd}$ term
The middle term in the expansion of $(1-\alpha x)^6$ is $4^{th}$ term
Given: $^4C_2\alpha^2$ = $-^6C_3\alpha^3$
$\Rightarrow\:\alpha=-\large\frac{^4C_2}{^6C_3}$ = $-\large\frac{6}{20}=-\large\frac{3}{10}$
answered Sep 17, 2013 by rvidyagovindarajan_1
 

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