To determine the number of non-real roots, you have to:
Determine the degree n of your polynomial - this is the highest power present in the polynomial.
Work out the multiplicity of zero as the root of your polynomial. Denote it by k.
Use Descartes' rule of signs to find the maximum possible number of positive and negative roots. Denote them by p and q, respectively.
Compute n - (k + p + q). This is the minimum number of non-real roots of your polynomial.
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