The correct option is D No solution
Case I When x>0,|x|=x
∴x2+15|x|+14=0 becomes
x2+15x+14=0
⇒x2+x+14x+14=0
⇒x=−1,−14…(i)
Case II When x<0,|x|=−x
∴x2+15|x|+14=0 becomes
⇒x2−15x+14=0
⇒x2−x−14x+14=0
⇒x(x−1)−14(x−1)=0
(x−1)(x−14)=0
⇒x=1,14…(ii)
From eqs. (i) and (ii) roots of given equation are not same. Therefore the given equation has no solution.