\(a_0 = 6, a_3 = 0\)
With integer coefficients, the irrational conjugates \(\sqrt2\) and \(-\sqrt3\) must also be roots. The polynomial is \((x^2-2)(x^2-3)=x^4-5x^2+6\). Hence \(a_0=6\) and \(a_3=0\).
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