An Algebra Challenge - Olympiad Mathematics

An Algebra Challenge - Olympiad Mathematics

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[pierreneau]

Solutions should be challenged by the value of (a) with 0, 2 or 4 solutions.

[johnstanley]

Note, LHS is zero at x=-1; so RHS requires a=1 or a = 0.5 to get zero on RHS; Choosing a=0.5 => x = (-1, +/-1.618), for a=1, x= (-1, 2, -1+/-1i)

[christopherrice]

What would happen if 'a' was an imaginary number or a complex number🤔?