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Let a and b be the solutions of the equation \(2x^2-10x+5=0\). What is the value of \((2a-3)(4b-6)\)?

 Feb 20, 2021

Best Answer 

 #1
avatar+944 
+2

Once again, we can use Vieta's equations. 

 

The sum of the roots is \(-\frac{b}{a} = -\frac{-10}{2} = 5\).

 

The product of the roots is \(\frac{c}{a} = \frac{5}{2}\).

 

Now, we can simplify: \((2a-3)(4b-6) = 8ab - 12(a+b) + 18 = 8(\frac{5}{2}) - 12(5) + 18 = \boxed{-22}\)

 Feb 20, 2021
 #1
avatar+944 
+2
Best Answer

Once again, we can use Vieta's equations. 

 

The sum of the roots is \(-\frac{b}{a} = -\frac{-10}{2} = 5\).

 

The product of the roots is \(\frac{c}{a} = \frac{5}{2}\).

 

Now, we can simplify: \((2a-3)(4b-6) = 8ab - 12(a+b) + 18 = 8(\frac{5}{2}) - 12(5) + 18 = \boxed{-22}\)

CubeyThePenguin Feb 20, 2021
 #2
avatar+294 
+3

Thank you!

calvinbun  Feb 23, 2021

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