Hi, airyie!

This problem has no solution. If is a root of a polynomial with real coefficients in one variable, then is also a root of that polynomial. This implies that, for your polynomial to have a root of , it must also have a root of . And, since the fundamental theorem of algebra states that a polynomial with complex coefficients of degree can have no more than complex roots, it follows that the polynomial sought in the problem must be of degree 4 or higher.

Now, if you want to find a fourth-degree polynomial with the given characteristics, you have the right idea: