Let \(a\) and \(b\) be the solutions of the equation \(2x^2+6x-14=0 \). What is the value of \((2a-3)(4b-6)\)?
Use Quadratic Formula to find roots (a and b) = - 3/2 +- sqrt(37) / 2
Use these values in (2a-3)(4b-6) to find the answer .....
By Vieta.......
The sum of the roots, a + b = -6/2 = -3
And the product of the roots = ab = -14/2 = -7
So
(2a - 3) ( 4b - 6) =
8ab - 12b - 12a + 18 =
8ab -12 ( a + b) + 18 =
8 (-7) - 12 ( -3) + 18 =
-56 + 36 + 18 =
-2
