Let a and b be the solutions of the equation 2x^2 + 6x - 14 = x^2 - 4x + 5. What is the value of (2a - 3)(4b - 6)?
Rearrange as
x^2 + 10x - 19 = 0
The sum of the roots = -10 / 1 = -10 = a + b
The product of the roots = -19/ 1= -19 = ab
(2a -3) ( 4b - 6) =
8ab - 12b - 12a + 18 =
8ab -12 ( a + b) + 18 =
8(-19) - 12(-10) + 18 =
-152 + 120 + 18 =
-14
