Results 1 to 3 of 3

Math Help - solutions for k values

  1. #1
    Member smmmc's Avatar
    Joined
    Jan 2009
    From
    House
    Posts
    80

    solutions for k values

    show that (k+1)x^2 -2x -k = 0 has a solution for all values of k.

    i used b^2-4ac=0

    i ended up with k=-2, not sure what the step is next

    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by smmmc View Post
    show that (k+1)x^2 -2x -k = 0 has a solution for all values of k.

    i used b^2-4ac=0

    i ended up with k=-2, not sure what the step is next

    thanks
    All you have to do is show that b^2 - 4ac \geq 0 for all values of k.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,686
    Thanks
    617
    Hello, smmmc!

    Show that (k+1)x^2 -2x -k \:=\: 0 has a solution for all values of k.

    i used b^2-4ac\:=\:0 . . Why zero?

    i ended up with k = -2 . . . . How?

    \text{We have: }\;\underbrace{(k+1)}_{a}x^2 + \underbrace{(-2)}_{b}x + \underbrace{(-k)}_{c} \:=\:0

    b^2-4ac \;=\;(-2)^2 - 4(k+1)(-k) \;=\; 4 + 4k^2 + 4k \;=\;4(k^2 + k + 1)

    And it can be shown that k^2 + k + 1 is always positive.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 11th 2011, 04:22 PM
  2. [SOLVED] Finding the values of k for which a matrix has no solutions
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 3rd 2011, 02:41 AM
  3. Replies: 3
    Last Post: January 24th 2011, 11:48 AM
  4. Replies: 6
    Last Post: July 26th 2010, 11:45 AM
  5. augmented matrix, number of solutions for values a,b,c
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 27th 2009, 08:45 PM

Search Tags


/mathhelpforum @mathhelpforum