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Math Help - Competition Question with Imaginary Roots

  1. #1
    Junior Member ReneG's Avatar
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    Competition Question with Imaginary Roots

    Came across this problem on a math competition.

    The equation 3x^2 + 4x + k = 0 has two imaginary roots. Which of the following is a true statement about the value of k?

    a) k < 0
    b) k < -2
    c) k > 2
    d) k > 0

    I'm having a hard time setting up a condition for k.
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  2. #2
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    Re: Competition Question with Imaginary Roots

    Quote Originally Posted by ReneG View Post
    Came across this problem on a math competition.
    The equation 3x^2 + 4x + k = 0 has two imaginary roots. Which of the following is a true statement about the value of k?
    a) k < 0
    b) k < -2
    c) k > 2
    d) k > 0
    I'm having a hard time setting up a condition for k.
    I am puzzled by this question because the correct answer is k>\frac{4}{3}~.

    Use the discriminate, b^2-4ac<0 or 16-12k<0.

    The closest answer is c). But that is not the exact answer.
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  3. #3
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    Re: Competition Question with Imaginary Roots

    I'm going to guess and say that the problem stated somewhere that k was an integer
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    Re: Competition Question with Imaginary Roots

    Surely the problem is not exactly as given here. The equation 3x^2+ 4x+ 4k= 0 can have complex roots but cannot have imaginary roots.
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    Re: Competition Question with Imaginary Roots

    Quote Originally Posted by HallsofIvy View Post
    Surely the problem is not exactly as given here. The equation 3x^2+ 4x+ 4k= 0 can have complex roots but cannot have imaginary roots.
    Whereas you are absolutely correct, I was part of the mathematics contest community long enough to know many in the mathematics education community use imaginary number and complex number interchangeably. I assure you it is futile to even try to correct them. Thus having seen that this is an old contest question, I assumed the worst.
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