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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 17, 2022
 #1
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Call the roots a, b

By Vieta

The sum ot the roots  =   a + b  = (3/2)......square both sides ⇒  a^2 + 2ab + b^2  = 9/4   (1)

The product of the  roots =  ab  = 29/2   ⇒       so    2ab  = 29    (2)

 

Sub (2)  into (1)

 

a^2  + 29   + b^2  =  9/4

 

a^2 + b^2  =  9/4   - 29

 

a^2  + b^2  =   -107 / 4

 

 

cool cool cool

 Apr 17, 2022

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