1. Tardigrade
  2. Question
  3. Mathematics
  4. The real roots of the equation x2+5|x|+4=0 are

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The real roots of the equation $ {{x}^{2}}+5|x|+4=0 $ are

Rajasthan PETRajasthan PET 2005

Solution:

Given, equation is $ {{x}^{2}}+5|x|+4=0 $
If $ x>0, $ then $ |x|=x $
$ \therefore $ $ {{x}^{2}}+5x+4=0 $
$ \Rightarrow $ $ {{x}^{2}}+4x+x+4=0 $
$ \Rightarrow $ $ (x+4)(x+1)=0 $
$ \Rightarrow $ $ x=-4,-1 $ If $ x < 0, $ then $ |x|=-x $
$ \therefore $ $ {{x}^{2}}-5x+4=0 $
$ \Rightarrow $ $ {{x}^{2}}-4x-x+4=0 $
$ \Rightarrow $ $ (x-4)(x-1)=0 $ $ \Rightarrow $ $ x=4,1 $
Hence, no real roots exist.