+230 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.
+1224 Let the roots of the quadratic be x and y.
sum of roots = \(-\frac{b}{a} = -\frac{-3}{2} = \frac{3}{2}\)
product of roots = \(\frac{c}{a} = \frac{27}{2}\)
sum of squares of roots = \(x^2 + y^2 = (x+y)^2 - 2xy = \frac{9}{4} - 27 = \boxed{-24.75}\)
