as f(x) is continous at x=0
at x=0- .. f(x) = K + [0-] = K-1
at x=0+... f(x) = [0+] = 0
as continous... K-1=0 ==> K=1
let one root be m and other be m+1
now, x = (-b+√b2-4ac)/2a and (-b-√b2-4ac)/2a = p and p+1
subtracting both..
√b2-4ac/a = (p+1) - p = 1
So, √b2-4ac = a