An inefficient root finder

Algebra Level 5

\[f( x ) =( { x }^{ 2 }+A ) ( { x }^{ 2 }+B )\]

If \(B-A=456\), find a real root for \(f( x )\) that satisfies the relation below, where \(C\) is a real, arbitrary constant.

\[x=\left( 1+i \right) \sqrt [ 4 ]{ \frac { 3 }{ 2 } { x }^{ 2 }+C }\]

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