A Polynomial with Two Square Roots

Algebra Level 5

Find the sum of all complex values of the parameter aa, for which the polynomial x4+(a21)x2+a3x^4+(a^2-1)x^2+a^3 has exactly two distinct complex roots.

Details and assumptions

You are not given any information about the multiplicity of each root.

Note: Real numbers are a subset of complex numbers.

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