If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax² + bx + 1 = 0 having real roots is

For quadratic equation to have real roots,

d≥ 0

b² – 4a ≥ 0

b² ≥ 4a

For a = 1, 4a = 4, b = 2, 3, 4 (3 equations)

With values of (a,b) as (1,2), (1,3), (1,4)

a = 2, 4a = 8, b = 3, 4 (2 equations)

With values of a,b as (2,3), (2,4)

a = 3, 4a = 12, b = 4 (1 equation)

With value of (a,b) as (3,4)

a = 4, 4a = 16, b = 4 (1 equation)

With values of (a,b) as (4,16)

Thus, total 7 equations are possible.