Question:hard
The inequality p^2+5 < 5p+14 can be satisfied if:
The inequality p^2+5 < 5p+14 can be satisfied if:
Show Hint
Rearrange into p^2 - 5p - 9 < 0, find its two roots, then test which option's stated range lies inside them.
Updated On: Jul 14, 2026
- p ≤ 6, p > -1
- p=6, p=-2
- p ≤ 6, p ≤ 1
- p ≥ 6, p=1
Show Solution
The Correct Option is A
Solution and Explanation
Substitution test: p=6 works, p=0 works, p=-0.9 works (option 1 range). p=-2 (option 2) fails. p=7 (option 4) fails. p=5 shows option 3 too narrow.
Final Answer: Option (1), p<=6, p>-1.
Final Answer: Option (1), p<=6, p>-1.
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