Elegant Eliminant

Algebra Level 3

Eliminate \(x\) from:

\(x^{2}+x=a\)

\(x^{3}=b\)

If the eliminant is of the form:

\(C_{0}a^{3}+C_{1}a^{2}b+C_{2}ab^{2}+C_{3}b^{3}\) \(+C_{4}a^{2}+C_{5}ab+C_{6}b^{2}+C_{7}a+C_{8}b+C_{9}=0\)

Compute: \(|\sum_{i=0}^9 C_{i}2^{9-i}|\)

NOTE: I) All \(C_{i}\)s are coprime. II) \(C_{i}\)s aren't binomial coefficients; Just arbitrary coefficients

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