Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201323 AprilOnline
Exam
JEE Main
Year
2013
Date
23 April
Mode
Online
Subject
Mathematics
Chapter
Basics of Mathematics

JEE Main 2013 · 23 April · Online · Mathematics · Basics of Mathematics

The least integral value α of x such that (x-5)/(x^2+5 x-14)>0 ,...

The least integral value α\alpha of xx such that x−5x2+5x−14>0\frac{x-5}{x^2+5 x-14}>0, satisfies :

Options

  1. Aα2+3α−4=0\alpha^2+3 \alpha-4=0
  2. Bα2−5α+4=0\alpha^2-5 \alpha+4=0
  3. Cα2−7α+6=0\alpha^2-7 \alpha+6=0
  4. Dα2+5α−6=0\alpha^2+5 \alpha-6=0

Correct answer

A. α2+3α−4=0\alpha^2+3 \alpha-4=0

Step-by-step solution

x−5x2+5x−14>0⇒x2+5x−14<x−5⇒x2+4x−9<0⇒α=−5,−4,−3,−2,−1,0,1\begin{aligned}& \frac{x-5}{x^2+5 x-14}>0 \Rightarrow x²+5 x-14 < x-5 \\ & \Rightarrow x²+4 x-9 < 0 \\ & \Rightarrow \alpha=-5,-4,-3,-2,-1,0,1 \end{aligned}\alpha=-5doesnotsatisfyanyoftheoptionsdoes not satisfy any of the options\alpha=-4satisfytheoption(a)satisfy the option (a)\alpha^2+3 \alpha-4=0$
Practice Basics of Mathematics on Quantrex Academy →

More from Basics of Mathematics

All Basics of Mathematics questions Full Basics of Mathematics list Basics of Mathematics JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs