Question:
The inequality p^2+5 < 5p+14 can be satisfied if:
The inequality p^2+5 < 5p+14 can be satisfied if:
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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
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The Correct Option is A
Solution and Explanation
Rearranged: p^2-5p-9<0. Roots: (5±sqrt(61))/2 = approx -1.405 and 6.405. Solution: -1.405<p<6.405. Option (1), p<=6, p>-1, lies entirely inside this range.
Final Answer: Option (1).
Final Answer: Option (1).
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