Question

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

• A. $15$
• B. $9$
• C. $7$
• D. $8$

Answer 1

The correct option is C $7$

$q^2-4p⩾0$
for $p,q\in \{1,2,3,4\}$
$(p,q)$ satisfying $q^2-4p⩾0$ are
$(1,4),(2,4),(3,4),(4,4),(1,3),(2,3),(1,2)$
$\therefore$ Seven such equations exist .