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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 14, 2020
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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.

 Dec 15, 2020

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