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.

Please help me quick! Thank you!

Guest Jul 15, 2019

#1**+4 **

What I would do is use the quadratic formula.

Then add the squares of the roots. You would get a real number.

Here is practice for complex solutions to quadratics if you are having trouble on these types

CalculatorUser Jul 15, 2019

#2**+1 **

2x^2 - 3x + 27

Call the roots a , b

The sum of these roots = - (-3/2) = 3/2

The product of these roots = 27/2

So

a + b = 3/2 (1)

ab = 27/2 (2)

Square both sides of (1)

a^2 + 2ab + b^2 = 9/4

a^2 + b^2 = 9/4 - 2ab sub in (2)

a^2 + b^2 = 9/4 - 2 (27/2)

a^2 + b^2 = 9/4 - 27

a^2 + b^2 = 9/4 - 108/4

a^2 + b^2 = - 99/4 = -24.75

CPhill Jul 15, 2019