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Let a and b be the solutions of the equation 2x^2+6x-14=0. What is the value of (2a-3)(4b-6)?

Guest Jul 19, 2022

Guest · Answer 1 · 2022-07-19T01:52:58

By the quadratic formula, the solutions are (-3 \pm sqrt(37))/2. Plugging them in, we get

(2(-3 + sqrt(37)/2 - 3)(4*(-3 - sqrt(37))/2 - 6) = -14

BuilderBoi · Answer 2 · 2022-07-19T02:29:05

Note that $(2a - 3)(4b - 6) = 8ab - 12b - 12a + 18 = 8ab - 12(a + b) + 18$

By Vieta, $a + b = {-6 \over 2} = -3$ and $ab = {-14 \over 2} = -7$

Plugging these in gives us ${8 \times -7 - 12(-3) + 18} = \color{brown}\boxed{-2}$

nerdiest · Answer 3 · 2022-07-19T01:58:52

look at builderboi's answer

nerdiest · Answer 4 · 2022-07-19T02:05:36

Use Quadratic Formula to find roots $a$ and $b$ $= - 3/2 +- \sqrt37 / 2$

Use these values in $(2a-3)(4b-6)$ to find the answer .....

which is also BuilderBoi's answer!