The quadratic 2x^2 - 3x + 27 = -4 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.
+14997 War die Summe der Quadrate diese Wurzeln?
Hallo Gast!
\(2x^2 - 3x + 27 = -4\\2x^2-3x+31=0\)
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
\(x = {3 \pm \sqrt{9-248} \over 2\cdot 2}\)
\(x = {3 \pm \sqrt{-239} \over 4}\)
\(\color{blue}x=(3\pm15.4596i)/4\)
\(x_1^2=(-230+92.7576i)/16\\ x_2^2=(-230-92.7576i)/16\)
\(\color{blue}x_1^2+x_2^2=-28.75\)
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