The coefficient of the 5th term in the binomial expansion of \((1 + kx)^{8}\), in ascending powers of x is \(\frac{35}{8}\). Find the value of the constant k.

A.

2

B.

\(\frac{1}{2}\)

C.

\(-\frac{1}{2}\)

D.

-2

Correct answer is B

\((1 + kx)^{8} = ^{8}C_{0}(1^{8})(kx)^{0} + ^{8}C_{1}(1^{7})(kx)^{1} + ...\)

The 5th term = \(^{8}C_{5 - 1}(1^{4})(kx)^{4}\)

= \(^{8}C_{4} (kx)^{4}\)

\(\implies 70k^{4} = \frac{35}{8}\)

\(k^{4} = \frac{\frac{35}{8}}{70}\)

\(k^{4} = \frac{1}{16}\)

\(k = \frac{1}{2}\)