Results 1 to 6 of 6

Math Help - Help me find k

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    3

    Help me find k

    a. the equation 3x^2 + 9x=17+6kx have roots that have equal magnitude but opposite in signs.
    b. the graph of y=x^2+kx+k+8 intersects the x axis at two distinct points.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by hirano View Post
    a. the equation 3x^2 + 9x=17+6kx have roots that have equal magnitude but opposite in signs.
    b. the graph of y=x^2+kx+k+8 intersects the x axis at two distinct points.
    Use the quadratic formula.

    (a)

    3x^2+9x=17+6kx\Rightarrow\ 3x^2+9x-6kx-17=0

    \displaystyle\ ax^2+bx+c=0\Rightarrow\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

    3x^2+(9-6k)x+(-17)=0

    For part (a), you require \pm(value), so the coefficient b needs to be zero.


    (b)

    x^2+kx+(k+8)=0

    The two points will be the same if b^2-4ac=0

    so you need to discover how b^2-4ac\ \ne\ 0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2010
    Posts
    3
    Dude I'm confused. Sorry

    a. Why the coefficient of b needs to be zero?

    b. So I will use > or < zero?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by hirano View Post
    Dude I'm confused. Sorry

    a. Why the coefficient of b needs to be zero?

    b. So I will use > or < zero?
    a. Is it possible to get "roots that have equal magnitude but opposite in signs" if b \neq 0 ....? Think about it.

    b. Obviously you use '> 0' (do you understand how the value of the discriminant relates to the number of solutions to a quadratic equation?)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2010
    Posts
    3
    a. I got it.

    b. so do I need to equate (k-8)(k+4)>0?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by hirano View Post
    a. I got it.

    b. so do I need to equate (k-8)(k+4)>0?
    Yes, that's it.
    The discriminant must be positive.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: March 22nd 2011, 04:57 PM
  2. Replies: 2
    Last Post: July 5th 2010, 08:48 PM
  3. Replies: 1
    Last Post: February 17th 2010, 03:58 PM
  4. Replies: 0
    Last Post: June 16th 2009, 12:43 PM
  5. Replies: 2
    Last Post: April 6th 2009, 08:57 PM

/mathhelpforum @mathhelpforum