Write a polynomial of least degree with real coefficients and with the root 8+2𝑖

Answer 1

If 8 + 2i is a root, then 8 - 2i MUST be a root. These only come in conjugate pairs. If these are the roots, then the factors must be:

[x - (8 + 2i)] and [x - (8 - 2i)]. To get the polynomial, just multiply these together. It will be easier to do by eliminating the inner parentheses:

(x - 8 - 2i)(x - 8 + 2i)

Multiplying this out you get: x² - 16x + 68 Note that you get terns that cancel out (16i and -16i for example) when you multiply these together. You also get -4i² which is the same as (-4)(-1) = 4.