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Math Help - Quadratic question!

  1. #1
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    Quadratic question!

    f(x) = x(squared) + kx + (k+3) where k is a constant. Given that the equation f(x) = 0 has qual roots..

    A) Find the possible values of k
    B) Solve f(x) = 0 for each possible value of k

    Given instead that k = 8

    C) Express f(x) in the form (x + a)squared + b, where a and b are constants.

    D) Solve f(x) = 0 giving your answers in surd form
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by cougar View Post
    f(x) = x(squared) + kx + (k+3) where k is a constant. Given that the equation f(x) = 0 has qual roots..
    should that be "equal roots"?

    if so, then

    A) Find the possible values of k
    B) Solve f(x) = 0 for each possible value of k
    you need the discriminant to be zero

    Given instead that k = 8

    C) Express f(x) in the form (x + a)squared + b, where a and b are constants.
    this is asking you to complete the square, do you know how to do that? (you can google it )

    D) Solve f(x) = 0 giving your answers in surd form
    use the quadratic formula. do you remember it?
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  3. #3
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    Sorry to ask, but I couldn't find anywhere what a 'qual root' is.

    About (C): if k=8, then f(x) = x^2 + 8x + 24

    Now you must use the fact that (a + b)^2 = a^2 + 2ab + b^2 \ (I), which is a particular case of Newton's Binomial. If you examine the expression for f(x), you can see that taking a = x and b = 4 and applying it to (I) seems promising. In fact:
    (x + 4)^2 = x^2 + 8x + 16
    Notice that it's not f(x) yet, but it's close. All you need to do now is adding 8:
    (x + 4)^2 + 8= x^2 + 8x + 16 + 8 = x^2 + 8x + 24 = f(x)
    And this answers your questions, a = 4 and b = 8. The name of this procedure is Square Completion. Check the link for further examples.

    For (D), I'll leave it to you with a tip: does what you just did in (C) helps you to find the roots? Or inform you whether they exist in \mathbb{R}?

    Regards,
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  4. #4
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    Yeh oops a typo, supposed to be equal. Thanks for the help YOU RULE
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