Question

The qudratic equation $x^2+15|x|+14=0$ has

• A. only positive solutions
• B. only negative solutions
• C. no solution
• D. both positive and negative solution

Answer 1

Answer: (C)

Case I : When $x>0,|x|=x$
$\therefore x^2+15|x|+14=0$ becomes
$x^2+15x+14=0$
$\Rightarrow x^2+x+14x+14=0$
$\Rightarrow x=-1,-14...(i)$
Case II : When $x<0,|x|=-x$
$\therefore x^2+15|x|+14=0$ becomes
$\Rightarrow x^2-15x+14=0$
$\Rightarrow x^2-x-14x+14=0$
$\Rightarrow x(x-1)-14(x-1)=0$
$\Rightarrow (x-1)(x-14)=0$
(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.