Question

If the sum of the coefficient in the expansion of ${(\alpha x^2-2x+1)}^{35}$ is equal to the sum of coefficients in the expansion of ${(x-\alpha y)}^{35}$, then $\alpha$ is equal to

• A. $2$
• B. $1$
• C. $-2$
• D. $-1$

Answer 1

The correct option is A $2$

Sum of the coefficients in the expansion of ${(\alpha x^2-2x+1)}^{35}=$Sum of the coefficients in the expansion of ${(x-\alpha y)}^{35}$

$Puttingx=y=1$

$\therefore {(\alpha -1)}^{35}={(1-\alpha )}^{35}$

$\Rightarrow {(\alpha -1)}^{35}={-(\alpha -1)}^{35}$

$\Rightarrow 2{(\alpha -1)}^{35}=0$

$\therefore \alpha -1=0$

$\therefore \alpha =1$