Let  $p,q\in \{1,2,3,4\}$   The number of equations of the form $p{x}^2+qx+1=0$ real  roots is 

Given $p, q \in \{1,2,3,4\}$ 

 To find, the number of equation of the form $p{x}^2+qx+1=0$

having real roots.  

  Equation  $p{x}^2+qx+1=0$  will have real root, if $D\ge 0$

  $\Rightarrow q^2-4\rho \ge 0$

 The number of solution of Eq. (i) is 

 $\left\{(q,p):p,q\in \{1,2,3,4\}\right.$ and 

  $=\left\{\right(4,4),(4,3),(4,2),(4,1),(3,2),(3,1\left)\right(2,1\left)\right\}$   

Hence, 7 equations can be formed, which satisfy the given condition