How do you write a polynomial of least degree with real coefficients and with roots 9 and 8+𝑖?

Question

Write your answer using the variable and in standard form with a leading coefficient of 1 please

Answer 1

The critical information here is that 8-i is also a root.

For polynomials with real coefficients, complex roots appear in conjugate pairs, i.e. if a+bi is a root, a-bi is also,

Therefore, this will be a 3rd degree (cubic) polynomial

[x-(8+i)][x-(8-i)](x-9)

[(x-8)² + 1](x-9)

(x² - 16x + 65)(x-9)

I will leave the last multiplication for you to do!