Question

The quadratic 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)

No solution

Case I When $x>0,|x|=x$
$\therefore x^2+15|x|+14=0$ becomes
$x^2+15x+14=0$
$\Rightarrow x^2+x+14x+14=0$
$\Rightarrow x=-1,-14\dots \left(i\right)$
Case II When $x<0,|x|=-x$
$\therefore x^2+15|x|+14=0$ becomes
$\Rightarrow x^2-15x+14=0$
$\Rightarrow x^2-x-14x+14=0$
$\Rightarrow x(x-1)-14(x-1)=0$
$(x-1)(x-14)=0$
$\Rightarrow x=1,14\dots \left(ii\right)$
From eqs. (i) and (ii) roots of given equation are not same. Therefore the given equation has no solution.