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Let \(a\) and \(b\) be the solutions of the equation \(2x^2+6x-14=0 \). What is the value of \((2a-3)(4b-6)\)?

 Dec 22, 2020
 #1
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Use Quadratic Formula to find    roots (a   and  b)  = - 3/2 +- sqrt(37) / 2

                                  Use these values in    (2a-3)(4b-6)      to find the answer .....

 Dec 22, 2020
 #2
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+2

By Vieta.......

 

The sum of the roots, a + b =  -6/2  = -3

And the product of the roots  = ab =  -14/2  =  -7

 

So

 

(2a - 3)  ( 4b - 6)   = 

 

8ab - 12b - 12a  + 18  =

 

8ab -12 ( a + b)  + 18   =

 

8 (-7)  - 12 ( -3)  +  18  =

 

-56  + 36  +  18  =

 

-2

 

cool cool cool

 Dec 22, 2020

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