CAT 2003 Slot 2 — QA Question 38
Discriminant and Roots of Quadratic EquationEasy
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:
Answer & solution
Correct answer: 7
- A
10
7
- C
6
- D
12
Solution
ax2 + bx + 1 = 0 … (i)
For equation (i) to have real roots, b2 − 4a ≥ 0
i.e. a ≤ b2/4 … (ii)
For b = 4: to satisfy (ii), a = 1, 2, 3, 4
∴ 4 equations are possible.
For b = 3: to satisfy (ii), a = 1, 2
∴ 2 equations are possible.
For b = 2: to satisfy (ii), a = 1
∴ 1 equation is possible.
Thus, total number of possible equations = 7
Hence, option (b).