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Q.
The coefficient of the middle term in the binomial expansion in powers of $x$ of $(1 +\alpha x)^4$ and of $(1 - \alpha x)^6$ is the same, then $-\alpha$ equals to
Binomial Theorem
Solution:
The middle term in the expansion of
$(1 + \alpha x)^4 = T_3 = \,{}^4C_2(\alpha x)^2 = 6\alpha^2 \,x^2$
The middle term in the expansion of
$(1 - \alpha x)^6 = T_4 = \,{}^6C_3(-\alpha x)^3 = -20\alpha^3 x^3$
According to the question
$6\alpha^2 = - 20 \alpha^3 $
$\Rightarrow \alpha = -\frac{3}{10}$