本题目来源于试卷: Complex Numbers，类别为 IB数学
[问答题]
Consider the equatio3x-: d,w dbdh3r s*5mm2jbexj nhv5gb)8-vz i *m :jyoj 2 $z^{4}+a z^{3}+b z^{2}+c z+d=0$ , where a, b, c, $d \in \mathbb{R} $ and $z \in \mathbb{C}$ . Two of the roots of the equation are $\log _{2}$ 10 and $\mathrm{i} \sqrt{5}$ and the sum of all the roots is $ 4+\log _{2} 5$ .
Show that 15 a+d+90=0 .
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