Question

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

• A. $-\frac{5}{3}$
• B. $-\frac{3}{5}$
• C. $-\frac{3}{10}$
• D. $-\frac{10}{3}$

Answer 1

The correct option is C

$-\frac{3}{10}$

Coefficient of Middle term in
$(1+\alpha x{)}^4=t_3{=}^4{C}_2.{\alpha }^2$
Coefficient of Middle term in
$(1-\alpha x{)}^6=t_4{=}^6{C}_3.(-\alpha {)}^3$
${}^4{C}_2{\alpha }^2={-}^6{C}_3{\alpha }^3\Rightarrow -6=20\alpha \Rightarrow \alpha =\frac{-3}{10}$