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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.

 Feb 22, 2021
 #1
avatar+944 
+1

Let the roots of the quadratic be x and y.

 

sum of roots = \(-\frac{b}{a} = -\frac{-3}{2} = \frac{3}{2}\)

 

product of roots = \(\frac{c}{a} = \frac{27}{2}\)

 

sum of squares of roots = \(x^2 + y^2 = (x+y)^2 - 2xy = \frac{9}{4} - 27 = \boxed{-24.75}\)

 Feb 22, 2021
 #2
avatar+118069 
+1

Call the roots a,b

Sum  of  the  roots  =   3/2  =   a+ b

Product of  the roots = ab  = 27/2   

2ab  =  2

 

a + b   =   3/2        square  both sides

 

a^2   + 2ab  + b^2  =  9/4

 

a^2  + 27  + b^2  = 9/4

 

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

 Feb 22, 2021

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