question_answer

If the quadratic equation \[f\,(x)=p{{x}^{2}}-qx+r=0\] has two distinct roots in (0, 2) where p, q, \[r\in N\] and \[f\,(1)=-1\] then the minimum value of p is

A) 1

B) 2

C) 4

D) none of these

Correct Answer: B

Solution :

\[f\,(1)=p-q+r=-1\]	?(i)
\[f\,(0)=r>0\]	?(ii)
\[f\,(2)=4p-2q+r>0\]	?(iii)
(ii) + (iii) \[\Rightarrow \]\[4p-2q+2r>0\]
\[2p-q+r>0\]
\[p+(p-q+r)>0\]      [using (i)]
\[p-1>0\]           \[\Rightarrow \]\[p>1\]
\[\therefore \]      \[p=2\]              \[(\because p\in N)\]