Question

Find the roots of the quadratic equation 12 abx2 – (9a2 – 8b2) x – 6ab = 0 in the variable x.

Answer 1

12abx2- 9a2x+ 8b2x -6ab
3ax (4bx -3a)+2b (4bx-3a)
(3ax+ 2b) (4bx-3a)=0
ie x = -2b/3a , 3a/4b

Answer 2

12abx² - (9a² - 8b²)x - 6ab = 0
12abx² - 9a²x - 8b²x - 6ab = 0
12abx² - 8b²x - 9a²x - 6ab = 0
4bx(3ax - 2b) -3a(3ax - 2b) = 0
(4bx - 3a) (3ax - 2b) = 0

4bx -3a =0 
4bx = 3a
x = 3a/4b ----------1

3ax -2b =0
3ax = 2b
x = 2b/3a-----------2

∴the value of x is 3a/4b or 2b/3a 

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