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Math Help - Using discriminant for seventeen degree polynomial

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    Using discriminant for seventeen degree polynomial

    I have seventeen degree polynomial. Can i know the number of roots from discriminant(>0,<0 or =0)...
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    Senior Member apcalculus's Avatar
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    Quote Originally Posted by fuaada View Post
    I have seventeen degree polynomial. Can i know the number of roots from discriminant(>0,<0 or =0)...

    If the degree is odd you know that there is at least one root from the Intermediate Value Theorem and the end behavior of odd-degreed polynomials. As far as I know a discriminant can only refer to the second-degree polynomial only.
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    Quote Originally Posted by apcalculus View Post
    If the degree is odd you know that there is at least one root from the Intermediate Value Theorem and the end behavior of odd-degreed polynomials. As far as I know a discriminant can only refer to the second-degree polynomial only.
    Discriminant - Wikipedia, the free encyclopedia

    Quote Originally Posted by fuaada View Post
    I have seventeen degree polynomial. Can i know the number of roots from discriminant(>0,<0 or =0)...
    If the discriminant is positive the polynomial will have 17 distinct real roots.

    If the discriminant is equal to zero, the polynomial will have repeated roots and therefore less than 17 distinct real roots. But there's no way of knowing how many distinct real roots there are.

    If the discriminant is less than zero, ..... I leave this case for you to research.
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    Thanks for the good reply....the informations are really helpful for me to go on with my research....
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