Find the range of values of k if has roots with the same sign .

My working :

let a and b be two roots of this equation .

If both a and b were positive , (a+b)>0 , thus -k+3>0 , and3>k

Similarly ab> 0 , thusk>0

If both a and b were negative , (a+b)<0 , thus -k+3<0 , then3<k

Similarly , ab>0 , thusk>0

So the range of values should be 3>k,k>0 , and 3<k .

But the answer given is k>0 only . So where is my mistake ?