Algebra

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!

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  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.

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