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Q.
The qudratic equation $x^2 + 15 |x| + 14 = 0$ has
WBJEEWBJEE 2010Complex Numbers and Quadratic Equations
Solution:
Case I : When $x>0,|x|=x$
$\therefore x^{2}+15|x|+14=0$ becomes
$x^{2}+15 x+14=0$
$\Rightarrow x^{2}+x+14 x+14=0$
$\Rightarrow x=-1,-14\,\,\,\,...(i)$
Case II : When $x<0,|x|=-x$
$\therefore x^{2}+15|x|+14=0$ becomes
$\Rightarrow x^{2}-15 x+14=0$
$\Rightarrow x^{2}-x-14 x+14=0$
$\Rightarrow x(x-1)-14(x-1)=0$
$\Rightarrow (x-1)(x-14)=0$
(ii) $\Rightarrow x=1,14\,\,\,....(ii)$
From Eqs. (i) and (ii) roots of given equation are not same. Therefore the given equation has no solution.