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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.

 

Please help me quick! Thank you! laugh

 Jul 15, 2019
 #1
avatar+2552 
+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

 Jul 15, 2019
edited by CalculatorUser  Jul 15, 2019
 #2
avatar+106539 
+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

 

 

cool cool cool

 Jul 15, 2019
 #3
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+1

Thanks a LOT!!!! laugh

 Jul 15, 2019

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