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Let a and $b$ be the roots of the equation 2x^2 - 7x + 2 = 0.$  Find (a - 1) + (b - 1).

 Aug 2, 2022

Best Answer 

 #2
avatar+2448 
0

Note that \((a - 1) + (b - 1) = a + b - 2\)

 

From Vieta's, we know that \(a + b = -{b \over a} = {7 \over 2} \)

 

So, \((a - 1) + (b - 1) = {7 \over 2} - 2 = \color{brown}\boxed{1.5}\)

 Aug 2, 2022
 #1
avatar+124676 
+2

2x^2 - 7x  + 2   = 0

 

sum of roots  =  7/2  = 3.5

product of roots  = 2/2  = 1

 

(a - 1) (b -1)  =  ab - (a+ b) + 1 =   1 - (3.5) + 1  =   -1.5

 

 

cool cool cool

 Aug 2, 2022
 #2
avatar+2448 
0
Best Answer

Note that \((a - 1) + (b - 1) = a + b - 2\)

 

From Vieta's, we know that \(a + b = -{b \over a} = {7 \over 2} \)

 

So, \((a - 1) + (b - 1) = {7 \over 2} - 2 = \color{brown}\boxed{1.5}\)

BuilderBoi Aug 2, 2022
 #3
avatar+124676 
+1

THX, BuilderBoi.....I didn't see the "+" sign  !!!

 

 

cool cool cool

CPhill  Aug 2, 2022

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