If both a and b belong to the set {1, 2, 3, 4}, then the number of equations

• Quant Quadratic

If both a and b belong to the set {1, 2, 3, 4}, then the number of equations of the form ax²+ bx + 1 = 0 having real roots is

1. 6
2. 7
3. 10
4. 12

Answer

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)

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

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

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

Thus, total 7 equations are possible.

The correct option is B.