Yahoo Answers is shutting down on 4 May 2021 (Eastern Time) and, as of 20 April 2021 (Eastern Time), the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

If -i is a zero of the polynomial k(x), then which of the following must be a factor of k(x) ?

A. i 

B. X^2ix+1 

C. X^2 -1 

D. X^2+1 

E. X^2 

4 Answers

Relevance
  • 1 month ago

    If x = -i is a root so is x = i

    so, x = ±i

    Hence, x² = -1

    i.e. x² + 1 = 0

    so, x² + 1 is a quadratic factor of k(x)

    :)>    

  • 1 month ago

    (x + i)

    If k(x) has all real coefficients, then (x - i) must also be a root, so therefore x^2 - i^2, which is x^2 + 1, is also a root. That's similar to answer D, except for some reason answer D uses a capital X, whereas the question uses a small x.

    But if k(x) can have non-real coefficients, then (x + i) is the only factor we know for sure.

  • rotchm
    Lv 7
    1 month ago

    Hint: then its conjugate is a root.

    Don't forget to vote me best answer for being the first to hint you through without spoiling the answer. That way it gives you a chance to work at it and to get good at it.

    If you were not Anonymous, I would hint further. 

  • 1 month ago

    If -i is a root then "i" is also a root (its conjugate).

    With two roots known, we can turn them into factors by subtracting them from "x":

    (x - i) and (x + i)

    The product of two factors will also be a factor, so:

    (x - i)(x + i)

    x² + xi - xi - i²

    x² - i²

    i² = -1, so:

    x² + 1

    This (answer D) will be a factor of k(x).

Still have questions? Get answers by asking now.