+379 Let a and b be the solutions of the equation \(2x^2-10x+5=0\). What is the value of \((2a-3)(4b-6)\)?
+1224 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: \((2a-3)(4b-6) = 8ab - 12(a+b) + 18 = 8(\frac{5}{2}) - 12(5) + 18 = \boxed{-22}\)
+1224 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: \((2a-3)(4b-6) = 8ab - 12(a+b) + 18 = 8(\frac{5}{2}) - 12(5) + 18 = \boxed{-22}\)
