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.

Guest Dec 1, 2019

edited by
Guest
Dec 1, 2019

#1**+1 **

\(x=\frac{3\pm \sqrt{9-4\times 2\times 27}}{4}\)

\(x=\frac{3+3\sqrt{23}i}{4}, \frac{3-3\sqrt{23}i}{4}\)

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

CoolStuffYT Dec 1, 2019