SOLUTION: For what real values of k does the quadratic 12x^2 + kx + 27 = 0 have nonreal roots? Enter your answer as an interval.

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Question 1209169: For what real values of k does the quadratic 12x^2 + kx + 27 = 0 have nonreal roots? Enter your answer as an interval.
Answer by ikleyn(52781) About Me  (Show Source):
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The quadratic equation 12x^2 + kx + 27 = 0 has nonreal roots if and only if its discriminant

    d = b^2 - 4ac

is negative

    k^2 - 4*12*27 < 0,

    k^2 < 4*12*27 = 4*3*4*3^3 = 3^4*4^2,

    |k| < sqrt%283%5E4%2A4%5E2%29 = 3^2*4 = 9*4 = 36,

    -36 < k < 36.


In the interval form, "k" should be in the interval (-36,36).    ANSWER

Solved.