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Let a and b be the solutions of the equation 2x^2 + 6x - 14 = x^2 - 4x + 5.  What is the value of (2a - 3)(4b - 6)?

 Jul 16, 2022
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Rearrange as

 

x^2 + 10x - 19 =  0

 

The sum of the roots =  -10 / 1 =  -10  =   a + b

 

The product of the roots =  -19/ 1=  -19 =  ab

 

(2a  -3) ( 4b - 6)   =

 

8ab - 12b - 12a + 18  =

 

8ab -12 ( a + b)  + 18  =

 

8(-19) - 12(-10)  + 18   =

 

-152 + 120 + 18  = 

 

-14

 

 

cool cool cool

 Jul 16, 2022

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