Binomial Theorem And Its Simple Applications Question 165
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
[IIT 1991; Pb. CET 1988]
Options:
A) 2
B) -1
C) 1
D) - 2
Show Answer
Answer:
Correct Answer: C
Solution:
- The sum of the coefficients of the 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 $
BETA
