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Math Help - Zeros of polynomials

  1. #1
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    Zeros of polynomials

    For some reason this is throwing me off.

    Given :

    Already found one zero at -1. Book has 3 zeros but given that it's degree 4 shouldn't it have 4 zeros?


    And how do I get the complex zeros?

    Sorry for having to use pics but i cant figure out the way you all do it yet
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  2. #2
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    Quote Originally Posted by aquavit View Post
    For some reason this is throwing me off.

    Given :

    Already found one zero at -1. Book has 3 zeros but given that it's degree 4 shouldn't it have 4 zeros?


    And how do I get the complex zeros?

    Sorry for having to use pics but i cant figure out the way you all do it yet
    1. Have a look here: http://www.mathhelpforum.com/math-he...-tutorial.html

    2. Actually there are 4 zeros if you count the -1 twice. The graph of the function touches the x-axis at x = -1. (In Germany such a case is considered to be a double-zero)
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by aquavit View Post
    For some reason this is throwing me off.

    Given :

    Already found one zero at -1. Book has 3 zeros but given that it's degree 4 shouldn't it have 4 zeros?


    And how do I get the complex zeros?

    Sorry for having to use pics but i cant figure out the way you all do it yet

    Using the rational roots theorem you discover that -1 is a root twice.

    Using synthetic division, you can factor the original polynomial down to:

    f(x)=(x-1)(x-1)(x^2-4x+8)

    Now use the quadratic formula to find your 2 complex roots.
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  4. #4
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    Awesome, i didn't realize -1 was mult.2, now if makes sense Thanks guys!
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