Results 1 to 5 of 5

Math Help - roots of polynomials

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    4

    roots of polynomials

    which of the following polynomials has roots 0, 1, and 2?


    help would be wonderful. thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Jen
    Jen is offline
    Member Jen's Avatar
    Joined
    Feb 2008
    From
    Corvallis, Oregon
    Posts
    157
    Quote Originally Posted by kalter View Post
    which of the following polynomials has roots 0, 1, and 2?


    help would be wonderful. thanks in advance.
    Consider what it means for a number to be a root of a polynomial...

    The following graphs depicts a polynomial with roots, x=-2 and x=1.

    Consider what happens to the value of y on the graph when x=-2 and when x=1

    roots of polynomials-capture.jpg

    Also consider that a polynomial of degree n, has at most n real roots.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    Posts
    4
    I'm not following. I haven't done this in ages.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Jen
    Jen is offline
    Member Jen's Avatar
    Joined
    Feb 2008
    From
    Corvallis, Oregon
    Posts
    157
    Quote Originally Posted by kalter View Post
    I'm not following. I haven't done this in ages.

    Notice on the graph where x=-2 and x=-1, y=0. For a number to be a root of a polynomial, it means that this is where it crosses the x-axis. This means that at that point, y=0.

    Does that help?

    Also for a polynomial of degree two (this means that the highest exponent is 2)there can be at most 2 real roots.

    Same for a polynomial of degree three, there can be at most three real roots.

    So considering that you need a polynomial that has those three roots, that should eliminate two of the choices you had.

    Does that make sense?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    May 2008
    Posts
    150
    Awards
    1
    Quote Originally Posted by kalter View Post
    which of the following polynomials has roots 0, 1, and 2?


    help would be wonderful. thanks in advance.
    Sub into the equation 0, 1 and 2. If you get 0, it means its a root!

    Example
    p(x) = x^2 + x + 2
    Sub in x = 1
    p(1) = 1 + 1 + 2 = 4
    So 1 is no a root of this equation because p(1) = 4

    Equation 2
    p(x) = x^3 - 3x^2 + 2x
    Sub in x = 2
    p(2) = (2)^3 -3(2)^2 + 2(2)
    p(2) = 8 - 12 + 4 which = 0
    therefore 2 is a root of p(x) = x^3 - 3x^2 + 2x

    Done by method of the 'factorial' theorem .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: April 7th 2011, 12:38 PM
  2. Roots of polynomials
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 4th 2010, 10:27 AM
  3. ROOTS and POLYNOMIALS
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 25th 2010, 03:40 AM
  4. Polynomials with many roots
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: August 1st 2008, 02:10 PM
  5. Roots of a sum of polynomials
    Posted in the Algebra Forum
    Replies: 0
    Last Post: March 24th 2008, 02:31 PM

Search Tags


/mathhelpforum @mathhelpforum