Question

Write a polynomial of least degree with real coefficients and with the root -6-8i. Write your answer using the variable x and in standard form with a leading coefficient of 1.

Thanks, I have no idea!

Answer 1

complex roots come in conjugate pairs, so if -6-8i is a root, so is -6+8i.

With those two roots, the least degree polynomial will just be degree 2, so we have

y = (x-(-6-8i))(x-(-6+8i))
= (x+6+8i)(x+6-8i)
= (x+6)^2 - (8i)^2
= x^2+12x+36+64
= x^2+12x+100

check here:

http://www.wolframalpha.com/input/?i=x^2%2B12x%2B100

scroll down a bit to where it shows the roots.