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# Help with cubic polynomial.

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A cubic polynomial $$z^3+az^2+bz+c$$ with integer coefficients has an integer solution. Which of the following cannot be a solution to this polynomial?

$$\frac{3}{2}+\frac{\sqrt{19}}{2}i$$

$$\frac{5}{2}+\frac{\sqrt{5}}{2}i$$

$$\frac{7}{2}+\frac{\sqrt{15}}{2}i$$

$$\frac{9}{2}+\frac{\sqrt{19}}{2}i$$

$$2-\sqrt{2}i$$

May 22, 2021