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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.

 Jan 25, 2021
 #1
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+1

 

 

Roots are 3/4 ± i 3/4√(23)    

        squared and added together = - 24.75

 Jan 25, 2021
 #2
avatar+116126 
+1

Call the roots a, b

 

The sumof the roots   = a +  b  =  3/2

Square this

a^2 + 2ab + b^2    = 9/4

 

The product of the  roots =  ab =   27/2  ⇒    2ab  =  27

 

So 

 

a^2  + 2ab  +  b^2  =   9/4

 

a^2  + 27  + b^2 =  9/4

 

a^2  + b^2   =  9/4  - 27  =    2.25  - 27   = -24.75

 

 

cool cool cool

 Jan 25, 2021

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