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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.

Sep 19, 2021

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2x^2 - 3x + 27 = -4 has two imaginary roots. What is the sum of the squares of these roots?

Hello Guest!

$$f(x)=2x^2 - 3x + 31 = 0$$

$$x = {-3 \pm \sqrt{3^2-4\cdot 2\cdot 31} \over 2\cdot 2}$$

$$x\in \{\frac{1}{4}(3+ i\sqrt{239}),\frac{1}{4}(3- i\sqrt{239})\}$$

$$\frac{1}{16}(3+ i\sqrt{239})^2+\frac{1}{16}(3- i\sqrt{239})^2=-\frac{115}{4}\color{blue}=-28.75$$

!

Sep 19, 2021