Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Find the complete solution set of the inequality 
≥ 0
A
B
C
∪ 
D
∪ 
Text Solution
Verified by ExpertsThe correct answer is:
D
For domain 21 – 4x – x 2 ≥ 0
⇒ x 2 + 4x – 21 ≤ 0 ⇒ (x + 7) (x – 3) ≤ 0 ⇒ x ∈ [–7, 3]
case-I : –7 ≤ x < –1 then 1– 
– ≤ 0
⇒ 1 ≤ 
⇒ x 2 + 4x – 20 ≤ 0 ⇒ (x + 2) 2 – 24 ≤ 0
⇒ (x + 2 + 2 
) (x + 2 – 2 
) ≤ 0 ⇒ x ∈ [–2 – 2 
, 2 
– 2]
∴ x ∈ [–2 –2 
, –1)
case-II : –1 < x ≤ 3 then 1 ≥ 21 – 4x – x 2
⇒ x 2 + 4x – 20 ≥ 0 ⇒ x ∈ (– ∞ , –2 – 2 
] ∪ [2 
– 2, ∞ )
∴ x ∈ 
x ∈ 
∪ 
──────────────────────────────────────────────────────────────────────────────────────────
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