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.

Guest Sep 19, 2021

#1**+1 **

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

**Hello Guest!**

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

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

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

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

!

asinus Sep 19, 2021