For what real values of k does the quadratic 12x^2 + kx + 27 = 8x^2 + 18 + 14x^2 + 32 have nonreal roots? Enter your answer as an interval.
12x^2 + kx + 27 = 8x^2 + 18 + 14x^2 + 32
Rearrange as
10x^2 - kx + 13 = 0
This will have non-real roots when the discriminant < 0
k^2 - 4(10)(13) < 0
k^2 < 520
k < sqrt (520) or k > -sqrt (520)
( -sqrt 520 , sqrt 520)
+1071 
