Question

If the sum of coefficient 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

Answer: (C)

1

Answer 2

The sum of coefficient of polynomial $(\alpha^{2}x^{2} - 2\alpha x + 1)^{51}$ is obtained by putting $x = 1$ in $(\alpha^{2}x^{2} - 2\alpha x + 1)^{51}$. Therefore by hypothesis $(\alpha^{2} - 2\alpha + 1)^{51}$ = 0 $\Rightarrow \alpha = 1$