# Complex+real?

Algebra Level 4

$(1+2i)x^{3}-2(3+i)x^{2}+(5-4i)x+2a^{2}=0$

Let $$a$$ be a real number, and the equation above have at least one real root (of $$x$$).

What is the value of $$\sum a^{2}$$?

Details and Assumptions:

• $$i^{2}=-1$$.

• $$\sum a^{2}$$ represents sum of squares of all possible values of $$a$$.

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