Question

Which polynomial of least degree has the roots 1, 2i

Answer 1

You just have to add them together.

Answer 2

And make it a polynomial

Answer 3

1 + 2i

Answer 4

to get a real co-efficient polynomial,
we need to have conjugate roots!

so if 2i is one if the root,
one more root must be -2i

so 3 roots, means the least degree will be 3.
3 roots are : 1, 2i, -2i

if 'a' is a root, (x-a) is a factor!

Answer 5

Do you understand?

Answer 6

so if 1 is the root, one of the factor is (x-1)

Answer 7

when 2i is the root, one of the factor is (x-2i)

what about,
when -2i is the root?