Question

If the third term in the binomial expansion of $(1+x{)}^m$ is -$\frac{1}{8}{x}^2$, then the rational value of m is

• A. 2
• B. $\frac{1}{2}$
• C. 3
• D. 4

Answer 1

The correct option is B

$\frac{1}{2}$

$m_{c_2}=-\frac{1}{8}\Rightarrow \frac{m(m-1)}{2}=-\frac{1}{8}\Rightarrow 4m^2-4m+1=0\Rightarrow (2m-1{)}^2=0\Rightarrow m=\frac{1}{2}$