If equations (a + 2)x 2 + bx + c = 0 and 2x 2 + 3x + 4 = 0 …

Maths Quadratic Equations Condition for Common Roots, Quadratic Expressions and Position of Roots Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If equations (a + 2)x 2 + bx + c = 0 and 2x 2 + 3x + 4 = 0 have a common root where a, b, c ∈ N then-

b 2 – 4ac < 0

Minimum value of a + b + c is 16

b 2 < 4ac + 8c

Minimum value of a + b + c is 7

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(b, c)

(a + 2)x 2 + bx + c = 0 ....(i)

2x 2 + 3x + 4 = 0 ....(ii)

for (ii) D < 0 ⇒ (i) and (ii) have both roots common.

∴

∴ for equation (i) D < 0

⇒ b 2 – 4c(a + 2) < 0 ⇒ b 2 < 4ac + 8c

⇒ k ∈ N, k ≥ 2

= k ⇒ a + b + c = 9k– 2

(a + b + c) min = 16

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