Find the number of equations having real roots. 
If both $a$ and $b$ belong to the set $\{1,2,3,4\}$ ,
  then number of equations of the form $ ax^2+bx+1=0$ having real roots is

$a.)\ 10\\
\color{green}{b.)\ 7}\\
c.)\ 6\\
d.)\ 12\\ $
To solve this I had to make a table and check each of the $16$ cases.
$$\begin{array}{|c|c|c|} \hline
 a & b & b^2-4a\geq 0 \\ \hline
1 & 1 & \\ \hline
1 & 2 & \checkmark \\ \hline
1 & 3 & \checkmark \\ \hline
1 & 4 & \checkmark \\ \hline
2 & 1 & \\ \hline
2 & 2 & \\ \hline
2 & 3 & \checkmark \\ \hline
2 & 4 & \checkmark \\ \hline
3 & 1 &  \\ \hline
3 & 2 &  \\ \hline
3 & 3 &  \\ \hline
3 & 4 & \checkmark \\ \hline
4 & 1 & \\ \hline
4 & 2 & \\ \hline
4 & 3 & \\ \hline
4 & 4 & \checkmark \\ \hline
\end{array}$$
But I would like to know if there is any short method for it.
I have studied maths up to $12$th grade, thanks.

For real roots, 
$b^2\ge{4a}$
Put $a=1$. 
$b^2\ge4$
$b$ can be $\{2,3,4\}$.
Now put $a=2$
$b$ can take two values.
Put $a=3$, $b$ can take one value and finally put $a=4$. Here $b$ can take one value.
Hence there are $7$ ordered pairs $(a,b)$ so there are $7$ such equations
