Write a polynomial function with rational coefficients so that P(x) = 0 has the given roots.
2i and radical 2

Question

Write a polynomial function with rational coefficients so that P(x) = 0 has the given roots.
2i and radical 2

accessdenied · Answer

You can start with naming the roots that they do not mention.  When we have a complex number, we also have its conjugate as a root.  When we have a root involving an irrational number, we also take its conjugate.
(The conjugate of a+bi being a-bi and the conjugate of a + bsqrt(c) being a - bsqrt(c)

From there, you just have to set up the equation with P(x) = (x-{first root})(x-{second root}) and so on for the third and fourth roots, and simplify by multiplying them together.