CGP Edu

Maths Quadratic Equations Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If x 2 + 6x – 27 > 0, –x 2 + 3x + 4 > 0, then x lies in the interval

(3, 4)

[3, 4]

(– ∞ , 3] ∪ [4, ∞ )

(−9, 4)

Text Solution

Verified by Experts

The correct answer is:

x 2 + 6x – 27 > 0

⇒ x 2 + 9x – 3x – 27 > 0

x(x + 9) –3(x + 9) > 0

⇒ (x – 3) (x + 9) > 0

x > 3 & x < – 9 ....(i)

–x 2 + 3x + 4 > 0

⇒ x 2 – 3x – 4 < 0

x 2 – 4x + x – 4 < 0

⇒ x(x – 4) +1 (x – 4) < 0

(x – 4) (x + 1) < 0 ⇒ –1 < x < 4 ....(ii)

from (i) and (ii)

(3, 4)

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