Question

If sum of the coefficients in the expansion of $(2+3cx+c^2{x}^2{)}^{12}$ vanishes, then $c$ equals to

• A. $-1,2$
• B. $1,2$
• C. $1,-2$
• D. $-1,-2$

Answer 1

Answer: (D)

$-1,-2$

sum of the coefficients in the expansion of $(2+3cx+c^2{x}^2{)}^{12}$ is obtained by putting $x=1$ in the given expression.

Since the sum of the co-efficients vanishes then,

$2+3c+c^2=0$

or, $(c+1)(c+2)=0$

or, $c=-1,-2$.