For real values of x, the expression will assume all real …

Maths Quadratic Equations Solution of Quadratic Inequations and Miscellaneous Equations Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

For real values of x, the expression will assume all real values provided -

a ≤ c ≤ b

b ≥ a ≥ c

b ≤ c ≤ a

a ≥ b ≥ c

Text Solution

Verified by Experts

The correct answer is:

y =

⇒ x 2 – (b + c + y) x + bc + ay – 0

D ≥ 0

⇒ (b + c + y) 2 –4 (bc + ay) ≥ 0

⇒ y 2 + 2(b + c – 2a) y + (b – c) 2 ≥ 0

D ≤ 0

⇒ 4(b + c – 2a) 2 – 4 (b – c) 2 ≤ 0

⇒ (2b – 2a) (2c – 2a) ≤ 0

⇒ (a – b) (a – c) ≤ 0

⇒ b ≤ a ≤ c if (b < c) or (c ≤ a ≤ b) if (c < b)

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