Question

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

• A. $2$
• B. $-1$
• C. $1$
• D. $-2$

Answer 1

The correct option is C $1$

${({\alpha }^2{x}^2-2\alpha x+1)}^{51}$

$x=1$

${({\alpha }^2-2\alpha +1)}^{51}=0$

$\alpha =2\ne 0$

$\alpha =-1\ne 0$

$\alpha =1=0$

$\alpha =-2\ne 0$