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Question:

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:

Explanation:

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).