The number of quadratic equations ax2+bx+c=0 such that ax2+bx+c+k=0 has two distinct positive roots for each k,where k is real

Dear sudarshan gupta, 

Given, ax²+bx+c+k=0, has two distinct positive roots for each k, where k is real

let, p,q be those  roots

then p and q are distinct and positive, hence product should be always positive for all real k

but pq=(c+k)/a, which can take both positive and negative values as k changes.

So there will be no quadratic equation ax²+bx+c = 0, such that ax²+bx+c+k=0 has 2 distinct positive roots for each real k.

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