We can find all the roots by factoring each polynomials.
Case A :
A = 2x^4 + x^3 + 5x^2 + 4x - 12
1 is an obvious Root of this polynomial :
2 * 1^4 + 1^3 + 5*1^2 + 4*1 - 12 = 12 - 12 = 0
Thus we have A= (2x^3+3x^2+8x+12)(x-1)
Lets go further now by factoring 2x^3 + 3x^2 + 8x + 12
We can simply group them :
(2x^3 + 3x^2) + (8x + 12) =
x²(2x+3) + 4(2x + 3) =
(2x+3)(x²+4)
To conclude : A = (2x+3)(x²+4)(x-1)
So the roots are : 1, -3/2, 2i and - 2i
Case B :
B = 2x^4 - x^3 + 5x^2 - 4x - 12
An obvious root here is -1 :
same principle applies, we write B = (2x^3−3x^2+8x−12)(x+1)
Finally B = (x²+4)(2x-3)(x+1)
And the roots are -1, 3/2, 2i and -2i
Good Luck
