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The quadratic 2x^2 - 3x + 21 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.

 Jul 1, 2021
 #1
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2x^2   -3x   +   21

 

Call the roots     r  and  s

 

Sum of  the roots =   3/2

r  +  s  = 3/2

Square both sides

r^2  +  2rs  +  s^2 =  9/4         (1)

 

Product of the roots  = rs

rs  =  21/2

2rs   =  21          (2)

 

Sub (2)  into (1)

 

r^2  +  21  +  s^2  =   9/4

 

r^2  + s^2   =  9/4 -  21

 

r^2  + s^2  =  9/4  -  84/4

 

r^2  + s^2   =   - 75 /  4  =  -18.75

 

 

cool cool cool

 Jul 1, 2021

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