The coefficient of the middle term in the binomial expansion in powers of $x$ of $(1+\alpha x)^4$ and of…
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 if $\alpha$ equals
$-\frac{5}{3}$
$\frac{3}{5}$
$\frac{-3}{10}$
$\frac{10}{3}$
Solution
Coefficient of Middle term in $(1+\alpha \mathrm{x})^4=\mathrm{t}_3={ }^4 \mathrm{C}_2 \cdot \alpha^2$
Coefficient of Middle term in $(1-\alpha \mathrm{x})^6=\mathrm{t}_4={ }^6 \mathrm{C}_3(-\alpha)^3$
$
{ }^4 \mathrm{C}_2 \alpha^2=-{ }^6 \mathrm{C}_3 \cdot \alpha^3 \Rightarrow-6=20 \alpha \Rightarrow \alpha=\frac{-3}{10}
$