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

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 7.

Option B is correct.

For quadratic equation to have real roots,  the discriminant, D = b^2 - 4ac, should be,

D ≥ 0

b^2 - 4a ≥ 0

b^2  ≥ 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)

3 + 2 + 1 + 1 =7

Therefore, a total of 7 equations are possible for a and b belonging to 1, 2, 3, 4 .