+0

0
36
4

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

Jul 19, 2022

#1
-1

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

Jul 19, 2022
#2
+2305
0

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 $${8 \times -7 - 12(-3) + 18} = \color{brown}\boxed{-2}$$

Jul 19, 2022
#3
+1113
+5

Jul 19, 2022
edited by nerdiest  Jul 19, 2022
#4
+1113
+5

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 .....