Question

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 

A. 10 

B. 7 

C. 6 

D. 12

Answer 1

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.