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Discriminant of quadratic equations

  1. Jul 23, 2009 #1
    I know this is probably really easy, but i just can't figure it out..

    1. The problem statement, all variables and given/known data

    Find values of k for which (5 + 4x - x^2 = k) has equal roots.

    I know the answer is k = 9 but i don't know how to get there..

    2. Relevant equations

    ax^2 + bx + c = 0
    Discriminant = b^2 - 4ac

    I know the discriminant has to equal 0 for the equation to have equal roots..

    3. The attempt at a solution

    But i get Discriminent = 36..?

    and the roots equaling -1 or 5..?

    Im lost.
     
  2. jcsd
  3. Jul 23, 2009 #2
    I got k = 9, please show me your work so i can check it out
     
  4. Jul 23, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, x^2- 4x- 5= 0 has discrimant 36 and roots -1 and 5 but that is NOT the equation you want- you've dropped the "k" which is the whole point of this problem! In order to write 5 + 4x - x^2 = k as "ax^2+ bx+ c= 0", subtract k from both sides and write it as -x^2+ 4x+ 5-k= 0. Now a= -1, b= 4, and c= 5-k. The discriminant is b^2- 4ac= (4)^2- 4(-1)(5-k). Set that equal to 0 and solve for k.
     
  5. Jul 23, 2009 #4
    HallsofIvy...

    Yep yep thats it...

    -x^2 + 4x + 5 - k = 0
    = 4^2 - 4(-1)(5-k)
    = 36 - 4k
    4k = 36
    k = 9

    Now i can sleep.... Thank you
     
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