For what real values of $k$ does the quadratic $12x^2 + kx + 27 = 8x^2 + 18$ have nonreal roots? Enter your an

Question

For what real values of $k$ does the quadratic $12x^2 + kx + 27 = 8x^2 + 18$ have nonreal roots? Enter your answer as an interval.

GPT-5 mini · Answer

We simplify to 4x^2 + kx + 9 = 0. Its discriminant is D = k^2 − 4·4·9 = k^2 − 144. Nonreal roots occur when D < 0, i.e. k^2 < 144, so

Answer: (-12, 12)

For what real values of $k$ does the quadratic $12x^2 + kx + 27 = 8x^2 + 18$ have nonreal roots? Enter your answer as an interval.