Question

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

• A. 1
• B. 2
• C. -1
• D. -2

Answer 1

The correct option is A 1

To find the sum of coefficients in any expansion, we put all variables as 1.
sum of coefficients = ${({\alpha }^2-2\alpha +1)}^{51}$
${({\alpha }^2-2\alpha +1)}^{51}=0{\alpha }^2-2\alpha +1=0\alpha =1$