Can you increase the degree of a polynomial with integer coefficients while keeping the exact same roots?

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Say I have a fifth degree polynomial $$z^5-5z^4-188z^3+986z^2+10152z-59696$$ with the roots $$ 7, 9-i,9 + i,-10 + 2i,-10 - 2i.$$ Say I want a sixth degree polynomial instead with the same roots. Can that be done?