Question

If the sum of the coefficients in the expansion of ${(a^2{x}^2-2ax+1)}^{51}$ vanishes, then the value of $a$ is

• A. $2$
• B. $-1$
• C. $1$
• D. $-2$

Answer 1

The correct option is C $1$

$(a^2{x}^2-2ax+1{)}^{51}=(ax-1{)}^{102}$
Now for sum of the coefficients put the value of $x=1$
Hence sum of the coefficients $=(a-1{)}^{102}$
Now for sum of the coefficients to be $0$
$a=1$