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Find k probably too easy

  1. Apr 1, 2009 #1
    Hi all,
    I have just an easy maths question which my brain is incapable of calculating for some reason...

    How would you find the value of k in: x^2 + 10x + k = 0?

    I have come up with (x+5)^2 +25=0, so is k=25? Is this correct?

    My maths knowledge has declined greatly in the duration of about 6 months...

    Thanks for any help :)
     
  2. jcsd
  3. Apr 1, 2009 #2

    Borek

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    Staff: Mentor

    I suppose you are not just looking for k, but for k such that the equation has 1 or 2 roots?
     
  4. Apr 1, 2009 #3

    thrill3rnit3

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    Gold Member

    Based from your given data, K can be....anything??

    Maybe you missed some other restriction, say, that the polynomial is a perfect square or something.
     
  5. Apr 1, 2009 #4
    Oops sorry, I forgot to mention that the equation has equal roots.
     
  6. Apr 1, 2009 #5
    If the quadratic has equal roots then the vertex will have to touch the x-axis. You can write your quadratic in this form: (x - c)^2 + d = 0, where c and d are some real numbers (which satisfy the equation, of course). Try completing the square and see if you can figure out the value of k to make the vertex touch the x-axis.
     
  7. Apr 1, 2009 #6
    Oops, you already have the right answer. You shouldn't get (x+5)^2 +25=0 though. You should have (x+5)^2 - (25 - k).
     
  8. Apr 1, 2009 #7
    If the quadratic equation ax^2 + bx + c = 0 has equal roots, then the descriminant = 0. That is, b^2 - 4ac = 0.

    Applying this to your question, we have:
    100 - 4 * 1 * k = 0
    100 - 4k = 0
    4k = 100
    k = 25.
     
  9. Apr 1, 2009 #8
    Another way you could solve this, just for kicks.

    x^2 + 10x + k = 0

    Corresponding to the coefficients of the standard form of a quadratic equation,

    a = 1
    b = 10
    c = k

    r1 = root one
    r2 = root two

    since the roots are equal, r = r1 = r2

    The sum of the roots:

    r + r = -b/a
    2r = -10/1
    r = -5

    The product of the roots:

    r * r = c/a
    r^2 = k/1
    (-5)^2 = k
    k = 25
     
  10. Apr 2, 2009 #9
    Thanks for the responses, problem solved :smile:
     
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