a maths question

let the roots be a & b
for 2 unequal roots
discriminant >0
(k+1)2-4(k+4)>0
k2-2k-3>0
(k-3)(k+1)>0
k>3 or k<-1

for -ve roots
a & b<0
a+b=k+1<0
k<-1

ab>0
k+4>0
k>-4
therefore-1>k>-4

x-1 x-2 x-3
x>3 + + + +
3>x>2 + + - -
2>x>1 + - - +
x<1 - - - -
therefore 3>x>2 or x<1