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NDA 2018 Maths · Mathematics · Quadratic Equations · medium

How many integers x satisfy the inequality x^2-5x-14<0?

Single correct option

How many integers xx satisfy the inequality x2−5x−14<0x^2-5x-14<0?
  1. A. 7
  2. B. 8
  3. C. 9
  4. D. 6
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Answer: (B) 8

Factorise: (x−7)(x+2)<0(x-7)(x+2)<0, so −2<x<7-2<x<7. The integers are −1,0,1,…,6-1,0,1,\dots,6, which are 8 in number. Including the endpoints −2-2 and 77 (strict inequality forbids them) gives the wrong count 10, and miscounting zero gives 7.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake