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Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

 Jan 13, 2024
 #1
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Simplify  as

 

x^2 + 12x - 4  =  0

 

We have the form ax^2 + bx + c = 0

 

Call the roots m , n

 

Product of the  roots  =  c / a =  -4/1  =  -4

 

mn  =-4 

2mn  = -8

 

Sum of the  roots   m + n  =  -b/a

 

m + n  = - 12/ 1 = -12

 

(m + n)^2  =  (-12)^2

 

m^2 + 2mn + n^2  = 144

 

m^2  - 8  + n^2  =144

 

m^2 + n^2 =  144 + 8 =   152 

 

cool cool cool

 Jan 13, 2024

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