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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.

 Dec 1, 2019
edited by Guest  Dec 1, 2019
 #1
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\(x=\frac{3\pm \sqrt{9-4\times 2\times 27}}{4}\)

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

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

 Dec 1, 2019
 #2
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how do I do that?

Guest Dec 2, 2019

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