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Q.
Let $p, q \in\{1,2,3,4\}$. The number of equation of form $p x^{2}+q x+1=0$ having real roots is $k$. Then find $k$.
Complex Numbers and Quadratic Equations
Solution:
Equation will have roots if $p^{2} \geq 4 q$
If $q=1$, then $p^{2} \geq 4 q$ for $p=2,3$ and $4$
$q=3$, then $p^{2} \geq 4 q$ for $p=4$
$q=2$, then $p^{2} \geq 4 q$ for $p=3$ and $p=4$
$q=4$, then $p^{2} \geq 4 q$ for $p=4$
Total $7$ possibilities.