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Sum of Coefficients of All Terms

If sum of coe...

Question

If sum of coefficient in expansion of $(2 + 3 c x + c^{2} x^{2})^{12}$ is $0$ . Then find the value of $c$ .

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Solution

For sum of coefficient in
$(2 + 3 c x + c^{2} x^{2})^{12}$
$\Rightarrow (C^{2} + 3 c + 2)^{12} = 0$
$\Rightarrow (C + 1) (C + 2) = 0$
$C = - 1, - 2$

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