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The quadratic 2x^2 - 3x + 29 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.

 Apr 26, 2021
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Call the  roots  m and  n

 

By Vieta's Theorem......

 

ax^2  + bc + c

 

Sum  of roots   = m + n  =  -b/a  =   3/2       square both sides   m^2 + 2mn + n^2  = 9/4   (1)

Product of  roots  = mn  =  c/a  =  27/2      and  2mn =  27    (2)

 

So......subbing   (2) into ( 1)   we have

 

m^2  +  27  + n^2  =  9/4

 

m^2 + n^2   =   9/4 - 27

 

m^2  + n^2   =  [9 - 108 ]  / 4   =   - 99 / 4

 Apr 26, 2021

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