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  4. The number of roots of the equation |x|=x2+x-4 is

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Q. The number of roots of the equation $ |x|={{x}^{2}}+x-4 $ is

KEAMKEAM 2007Complex Numbers and Quadratic Equations

Solution:

The given equation is $ |x|={{x}^{2}}+x-4 $ If $ x\ge 0,x={{x}^{2}}+x-4 $
$ \Rightarrow $ $ {{x}^{2}}-4=0\Rightarrow x=\pm 2 $
$ \therefore $ We take, $ x=2 $ (neglect $ x=-2 $ ) and
if $ x<0 $ $ -x={{x}^{2}}-x-4 $
$ \Rightarrow $ $ {{x}^{2}}=4\Rightarrow x=\pm 2 $
$ \therefore $ We take $ x=-2 $ (neglect $ x=2 $ )
Thus, the number of roots of given equation is 2.