lie in the same region of lines x+2y−5=0 and 3x−y+1=0 (k2+2(k+1)−5)<0 and 3k2−(2k+1)+1>0 ⇒k2+2k−3<0 and 3k2−k>0 (k+3)(k−1)<0 and k(3k−1)>0 k∈(−3,1) and k∈(−∞,0)∪(
1
3
,∞) ∴k∈(−3,0)∪(
1
3
,1) Integral value of k{−2,−1} ∴ Possible number of points is 2.