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.
+1253 \(x=\frac{3\pm \sqrt{9-4\times 2\times 27}}{4}\)
\(x=\frac{3+3\sqrt{23}i}{4}, \frac{3-3\sqrt{23}i}{4}\)
Square both to get
\(x^2=\frac{-198+12\sqrt 23i}{16}, \frac{-198-12\sqrt 23i}{16} \)
Now just add them up.
You are very welcome!
:P
