UPSC 2016 CDS II Math Paper

The quadratic equation x2+ax+b=0 has real roots if
D=a2−4b≥0
⇒a2≥4b
when b=1,a2≥4
The possible set of values of a are 2, 3 and 4.
When b=2,a2≥8
The possible set of values of a are 3 and 4.
When b=3,a2≥12
The possible set of value of a is 4.
When b=4,a2≥16
The possible set of value of a is 4. Thus, the possible pairs of values of a and b are 7.