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# Help. Thank you.

+3
75
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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

#1
+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
+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: $$(2a-3)(4b-6) = 8ab - 12(a+b) + 18 = 8(\frac{5}{2}) - 12(5) + 18 = \boxed{-22}$$

CubeyThePenguin Feb 20, 2021
#2
+294
+3

Thank you!

calvinbun  Feb 23, 2021