Question

a 2 x 2 - 3abx + 2b 2 = 0 find the roots of the quadratic equation by method of completing the square

Answer 1

a²x²-3abx+2b²=0
or, {(ax)²-2.ax.3b/2+(3b/2)²}+2b²-9b²/4=0
or, (ax-3b/2)²+(8b²-9b²)/4=0
or, (ax-3b/2)²-(b/2)²=0
or, (ax-3b/2+b/2)(ax-3b/2-b/2)=0
or, (ax-b)(ax-2b)=0
Either, ax-b=0
or, ax=b
or, x=b/a
Or, ax-2b=0
or,  ax=2b
or, x=2b/a
∴, the roots of the given equations are: b/a, 2b/a. Ans.

Answer 2

a²x²-3abx+2b²=0

or, {(ax)²-2.ax.3b/2+(3b/2)²}+2b²-9b²/4=0

or, (ax-3b/2)²+(8b²-9b²)/4=0

or, (ax-3b/2)²-(b/2)²=0

or, (ax-3b/2+b/2)(ax-3b/2-b/2)=0

or, (ax-b)(ax-2b)=0

Either, ax-b=0

or, ax=b

or, x=b/a

Or, ax-2b=0

or,  ax=2b

or, x=2b/a

∴, the roots of the given equations are: b/a, 2b/a. Ans.