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Math Help - help producing eigenvlaues

  1. #1
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    help producing eigenvlaues

    hi i worked out a matrix of this form



    call lambda x

    (2-x ) 0 3
    0 (6-x) -3
    3 -3 (2-x)

    and that formula below was what i got

    -x^3 + 10x^2 - 10x - 48

    but this doesnt look right as i cant find the roots. I would be really grateful if someone would verify i have worked it out correctly.
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  2. #2
    Senior Member Peritus's Avatar
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    First of all you should always remember that if you arrive at some expression you can't solve it doesn't mean that it's not correct, get yourself free from this limiting way of thinking which is the result of improper teaching methods.

    I've rechecked your solution, and your characteristic polynomial is correct.
    Now if only you could have one root of this polynomial you could reduce it to a second degree polynomial by means of long division which you could readily solve. Fortunately there's a simple method to find this root:

    Rational root theorem - Wikipedia, the free encyclopedia

    to assure you that this method in fact works try substituting 8 into your equation.
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  3. #3
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    thank you , your restored my confidence!

    one last question, if i plot this function, it looks like it pass through the X axis three times, this does mean it should have 3 roots?
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  4. #4
    Senior Member Peritus's Avatar
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    Quote Originally Posted by jonbob81 View Post
    one last question, if i plot this function, it looks like it pass through the X axis three times, this does mean it should have 3 roots?
    Not exactly, what it means is that it has 3 real roots.
    For example let's look at the following function:

    x^5  - 12x^4  + 12x - 6x^2  + 11x - 6

    if you plot it over the real numbers axis you'll see that passes through the x axis three times, but in fact it has 5 roots 2 of which are imaginary:

    Fundamental theorem of algebra - Wikipedia, the free encyclopedia
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