Question

If the sum of the coefficients in the expansion of ${(a^2{x}^2-6ax+11)}^{10}$, where $a$ is constant is $1024$, then the value of $a$ is:

• A. $5$
• B. $1$
• C. $2$
• D. $3$
• E. $4$

Answer 1

The correct option is D

$3$

Explanation for the correct option.

The given expression is ${(a^2{x}^2-6ax+11)}^{10}$.

For the sum of coefficients, we will take $x=1$.

$\begin{array}{rcl}{\Rightarrow (a^2-6a+11)}^{10}& =& 1024\\ {\Rightarrow (a^2-6a+11)}^{10}& =& 2^{10}\\ \Rightarrow a^2-6a+11& =& 2\\ \Rightarrow a^2-6a+9& =& 0\\ \Rightarrow {\left(a-3\right)}^2& =& 0\\ \Rightarrow a& =& 3\end{array}$

Hence, option D is correct.