if these two equations have a common root then find the other ?

Let x = a be the common root

=> ma^2 + 27a - 28 = 0 ... ( 1 )

and 2ma^2 - a - 12 = 0 ... ( 2 )

Multiplying eqn. ( 1 ) by 2 and subtracting eqn. ( 2 ) from it,

55a = 44

=> a = 4/5

Plugging a = 4/5 in ( 2 )

2m(4/5)^2 - 4/5 - 12 = 0

=> (32/25) m = 64/5

=> m = 10

Plugging m = 10 in given eqn.,

10x^2 + 27x - 28 = 0

=> 10x^2 - 8x + 35x - 28 = 0

=> 2x (5x - 4) + 7 (5x - 4) = 0

=> (2x + 7) (5x - 4) = 0

=> the other root is - 7/2

Plugging m = 10 in the second given eqn.,

20x^2 - x - 12 = 0

=> 20x^2 - 16x + 15x - 12 = 0

=> 4x (5x - 4) + 3 (5x - 4) = 0

=> (4x + 3) (5x - 4) = 0

=> the other root is - 3/4

Answer:

Different roots are x = - 7/2 and x = - 3/4.

let the common root be a

so ma^2 + 27a - 28 =0 --------------------(I)

and 2ma^2 - a - 12 =0----------------------(II)

solving (I) & (II) we have

2ma^2 + 54 a - 56 =0

2ma^2 - a - 12 =0

so 55a = 44 so a = 44/55= 4/5

so from(I) & (II)

2m( 4/5)^2 - 4/5 - 12 =0

32 m/25 - 4/5 - 12 =0

32 m - 20 - 300 =0

or 32m = 320

or m= 10

10 x^2 + 27x - 28 =0

or 10 x^2 + 35x - 8 x- 28 =0

or 5x( 2x + 7) - 4( 2x+ 7) =0

or (5x-4) ( 2x + 7) =0

so x= 4/5 common root & x= - 7/2 the other root ANSWER