Question 1209169
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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(3^4*4^2)}}} = 3^2*4 = 9*4 = 36,

    -36 < k < 36.


In the interval form, "k" should be in the interval (-36,36).    <U>ANSWER</U>
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Solved.