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Middle Terms

The coefficie...

Question

The coefficient of the middle term in the binomial expansion in powers of x of ${(1 + α x)}^{4}$ and of ${(1 - α x)}^{4}$ is the same if α =

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Solution

The correct option is C
Given $^{4} C_{2} α^{2} =^{6} C_{3} {(- α)}^{3} \Rightarrow 6 α^{2} = - 20 α^{3} \Rightarrow α = \frac{- 3}{10}$

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The coefficient of the middle term in the binomial expansion in powers of x of $(1 + α x)^{4}$ and of $(1 - α x)^{6}$ is the same if $α$ equals

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