Write a polynomial function

Question

Write a polynomial function of least degree with rational coefficients so that

​P(x)=0

has the given roots.

7i​,

7−i

Answer 1

The complex conjugate of complex roots must also be roots, so your minimum set of roots is

7i

-7i

7 - i

7 + i

P(x) = A(x - 7i)(x + 7i)[x - (7 - i)][x - (7 + i)],

where A is real, rational, and A ≠ 0.