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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.

 Jun 29, 2021

Best Answer 

 #1
avatar+35059 
+2

2x^2 - 3x + 29     divide through by 2

 

x^2 - 3/2x + 29/2       roots   r and s   SUM to -3/2   and multiply  to  29/2

 

Now:

(r+s)^2   = r^2 + s^2 + 2rs    sub in the values above

   (-3/2)^2 = r^2 + s^2  + 2 ( 29/2) 

 

r^2 + s^2 =   (-3/2)^2 - 2 ( 29/2)            You can finish !            

 Jun 29, 2021
 #1
avatar+35059 
+2
Best Answer

2x^2 - 3x + 29     divide through by 2

 

x^2 - 3/2x + 29/2       roots   r and s   SUM to -3/2   and multiply  to  29/2

 

Now:

(r+s)^2   = r^2 + s^2 + 2rs    sub in the values above

   (-3/2)^2 = r^2 + s^2  + 2 ( 29/2) 

 

r^2 + s^2 =   (-3/2)^2 - 2 ( 29/2)            You can finish !            

ElectricPavlov Jun 29, 2021

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