The roots a and b of the quadratic equation x2+kx+12=0 are such that a-b=1. determine k.

Simplifying 
x2+kx + -12=0

Recorder the terms: -12+kx+x2 =0

solving: -12+ kx + x2=0

now solving for variable 'K'

move all the terms containing K to the left, all other terms to the right.

Add '12' to each side of the equation.
-12+12+kx+ x2 =0+12

combine like terms: -12+12=0
0+kx +x2=0+12
 
combine like terms:  0+12=12
kx+x2+-1x2= 12 + -1x2

combine like terms: x2 + -1x2=0
kx+0 =12+-1x2
kx= 12+-1x2

divide each side by 'x'.
k=12x-1 + x

simplifying:  K=12x -1 +-1x

Anw: K=12x -1+ -1x