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Math Help - Finding All Real Zeros

  1. #1
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    Finding All Real Zeros

    It says find all real zeros of the function f(x) = x^5-x^4-7x^3+11x^2-8x+12. I searched all over but everywhere I check is saying to use this theorem thing with the negative signs but our teacher didn't teach us about that, she told us to use a graphing calculator. But I'm confused because the only answers I could find were 2, and -3 but since the highest exponent is 5, shouldn't I have 5 answers?
    Last edited by AnnaLena224; December 10th 2009 at 04:16 PM. Reason: mistake
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  2. #2
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    Quote Originally Posted by AnnaLena224 View Post
    It says find all real zeros of the function f(x) = x^5-x^4-7x^3+11x^2-8x+12. I searched all over but everywhere I check is saying to use this theorem thing with the negative signs but our teacher didn't teach us about that
    Was it called the factor theorem?


    Quote Originally Posted by AnnaLena224 View Post
    But I'm confused because the only answers I could find were 2, and -3 but since the highest exponent is 5, shouldn't I have 5 answers?
    2 and -3 could be repeated factors.

    Have a go at x^5-x^4-7x^3+11x^2-8x+12 \div (x-2)(x+3)

    Then try to factor the quotient.
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  3. #3
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    I factored it and got
    x^3-2x^2+x-2
    x^2(x-2) 1(x-2)
    (x-2)(x^2+1)
    x=2
    x=i(square root)1
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  4. #4
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    Quote Originally Posted by AnnaLena224 View Post
    I factored it and got
    x^3-2x^2+x-2
    x^2(x-2) 1(x-2)
    (x-2)(x^2+1)
    x=2
    x=i(square root)1
    Therefore your factors are 2,2,-3,i,-i
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  5. #5
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    Quote Originally Posted by pickslides
    Was it called the factor theorem?
    I think the poster might be talking about Descartes rules of signs in reference to the negative sign comment.
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