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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)?

 Jul 19, 2022
 #1
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-1

By the quadratic formula, the solutions are (-3 \pm sqrt(37))/2.  Plugging them in, we get

(2(-3 + sqrt(37)/2 - 3)(4*(-3 - sqrt(37))/2 - 6) = -14

 Jul 19, 2022
 #2
avatar+2448 
-1

Note that\((2a - 3)(4b - 6) = 8ab - 12b - 12a + 18 = 8ab - 12(a + b) + 18\)

 

By Vieta, \(a + b = {-6 \over 2} = -3\) and \(ab = {-14 \over 2} = -7\)

 

Plugging these in gives us \({8 \times -7 - 12(-3) + 18} = \color{brown}\boxed{-2}\)

 Jul 19, 2022
 #3
avatar+1155 
+5

look at builderboi's answer

 Jul 19, 2022
edited by nerdiest  Jul 19, 2022
 #4
avatar+1155 
+5

Use Quadratic Formula to find roots \(a\) and \(b\) \( = - 3/2 +- \sqrt37 / 2\)

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

 

 

which is also BuilderBoi's answer! laugh

 Jul 19, 2022

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