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**mathaddict** Find the range of values of k if $\displaystyle x^2+(k-3)x+k=0$ has roots with the same sign .

My working :

$\displaystyle x^2+(k-3)x+k=0$

let a and b be two roots of this equation .

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

Similarly ab> 0 , thus **k>0**

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

Similarly , ab>0 , thus **k>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 ?