Results 1 to 2 of 2

Thread: Zero's of polynomial [Rolles Theorem]

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    14

    Zero's of polynomial [Rolles Theorem]

    Prove that if p(x) is a polynomial with n distinct zeros then p'(x) has at least n-1 zeros.

    It seems that this is a fairly simply use of Rolle's theorem but I can't seem to see how to do it! Help would be great!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by nlews View Post
    Prove that if p(x) is a polynomial with n distinct zeros then p'(x) has at least n-1 zeros.

    It seems that this is a fairly simply use of Rolle's theorem but I can't seem to see how to do it! Help would be great!
    Here is an idea on how to get started. To simplify thing lets suppose that $\displaystyle p(x)$ has two roots lets call them $\displaystyle x_1,x_2$ and with out loss of generality we can have $\displaystyle x_1 < x_2$.

    Rolle's theorem states that if $\displaystyle p(x_1)=p(x_2)=0$ then $\displaystyle p'(c)=0$ for some $\displaystyle c \in (x_1,x_2)$.

    The above statement proves that if $\displaystyle p(x)$ has two roots then $\displaystyle p'(x)$ has $\displaystyle 2-1=1$ roots.

    See if you can generalize this argument.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rolles Theorem
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Mar 31st 2011, 11:00 PM
  2. Rolles Theorem
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 14th 2010, 03:48 AM
  3. Rolles Theorem
    Posted in the Calculus Forum
    Replies: 15
    Last Post: Apr 1st 2010, 11:53 AM
  4. Rolles Theorem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Mar 29th 2010, 03:47 PM
  5. Rolles Theorm
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Mar 25th 2010, 05:06 PM

Search Tags


/mathhelpforum @mathhelpforum