Algebra Level 4

$\left| \begin{array}{} (1+\alpha)^2 & (1+2\alpha)^2 & (1+3\alpha)^2 \\ (2+\alpha)^2 & (2+2\alpha)^2 & (2+3\alpha)^2 \\ (3+\alpha)^2 & (3+2\alpha)^2 & (3+3\alpha)^2 \\ \end{array} \right|=-648\alpha$
Which of the following values of $$\alpha$$ satisfy the above equation ?
$\begin{array}{} (1) \, -4 \quad \quad \quad \quad & (2) \, 9 \\ (3) \, -9 & (4) \, 4 \end{array}$
Note :

• Submit your answer as the increasing order of the serial numbers of all the correct options.

• For eg, if your answer is $$(1),(2)$$, then submit 12 as the correct answer, if your answer is $$(2),(3),(4)$$, then submit 234 as the correct answer.

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