The quadratic $2x^2-3x+27$ has two imaginary roots. What is the sum of the squares of these roots? Express your answer as a decimal rounded to the nearest hundredth.
By the quadratic formula, x = (3 pm 3i sqrt(23))/4. Then ((3 + 3i sqrt(23))/4)^2 + ((3 - 3i sqrt(23))/4)^2 = -11/4.
