Question

The number of points $(p,q)$ such that $p,q\in \{1,2,3,4\}$ and the equation $p{x}^2+qx+1=0$ has real roots is

• A. $7$
• B. $8$
• C. $9$
• D. none of these

Answer 1

The correct option is A $7$

$p{x}^2+qx+1=0$ has real roots
if $q^2-4p\ge 0or{q}^2\ge 4p$
Since $p,q\in \{1,2,3,4\}$
The required points are
$(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(4,4)$
So the required number is $7$.