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# If $p,q\in \{1,2,3,4\},$ then the number of equations of the form $px^2+qx+1=0$ having real roots is?

(A) 15 (B) 9 (C) 8 (D) 7

Since it is given that the roots of $px^2+qx+1=0$  are real,

$q^2\geq 4p$

$\therefore\:$  the choices of $p\:and\:q$  are as below.

 p 1 2 3 4 q 2,3,4 3,4 4 4
$\therefore\:$  the total number of equations=$3+2+1+1=7$

edited Aug 6, 2013