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The quadratic equation $3x^2+4x-9 = 2x^2-6x+1$ has two real roots. What is the sum of the squares of these roots?

 Aug 30, 2023
 #1
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3x^2+4x-9 = 2x^2-6x+1  rearrange as

 

x^2 + 10x - 10   =  0

 

By Vieta

 

Call the roots a and  b

 

The sum of the roots =   -10/1   =  -10

 

So

a +b  =  -10     squsre both sides

 

a^2 + 2ab  + b^2   =100     (1)

 

And the product of the roots =  -10/1  = -10

 

So

 

ab =  -10     and       2ab   =  -20    (2)

 

Sub (2)  into (1)

 

a^2  - 20  + b^2 =  100

 

a^2 + b^2  =   120   =    the sum of the squares of the roots

 

 

cool cool cool 

 Aug 30, 2023

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