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Let r and s be the roots of x^2 - 6x + 2 = 14.  Find (r - s)^2.

 Apr 15, 2022
 #1
avatar+122390 
+1

x^2 - 6x + 2 - 14  =  0

 

x^2  - 6x - 12   = 0

 

By Vieta, the sum of the roots  =  - (-6) / 1  = 6

So ...    r + s  = 6     square both sides

r^2 + 2rs + s^2  =   36     

r^2 + s^2  =  36 - 2rs (1)

 

 

And the product of the roots =  -12 /1 =  -12

So.....  rs = -12

So   2rs  = -24     (2)

 

 

So

 

( r - s)^2  =  r^2 - 2rs + s^2

 ( r -s)^2  = ( r^2 + s^2)  -  2rs         sub in (1)  and (2)

(r - s)^2  =  (36 - 2rs) - 2rs

(r - s)^2  =  (36 - -24) - (-24)

(r -s)^2  =  60 + 24  =   84

 

cool cool cool

 Apr 15, 2022
 #2
avatar+1384 
0

Chris will do everything BUT won't solve the equation... LOL!!!

BuilderBoi  Apr 15, 2022

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