Question 24Let $P(z)=z^8+(4\sqrt{3}+6)z^4$ $-(4\sqrt{3}+7).$ What is the minimum perimeter among all the $8$-sided polygons in the complex plane whose vertices are precisely the zeros of $P(z)?$$4\sqrt{3}+4$$8\sqrt{2}$$3\sqrt{2}+3\sqrt{6}$$4\sqrt{2}+4\sqrt{3}$$4\sqrt{3}+6$