• # 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

 $f\,(1)=p-q+r=-1$ ?(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$ $\therefore$      $p=2$              $(\because p\in N)$