Question

The number of real solutions of the equation |x|² + 5|x| + 4 = 0 is

• (A) 0
• (B) 1
• (C) 2
• (D) 3

Answer 1

The Correct Option is A

Explanation:
Given: $|x{|}^2+5|x|+4=0$Case I: If $x\ge 0,$ then $|x|=x$ and $x^2+5x+4=0$ $(x+1)(x+4)=0\Rightarrow x=-1,-4(<0)$Thus, there is no solution of the equation when $x\ge 0$ Case $\Vert :$ If $x<0,$ then $|x|=-x$The equation is $x^2-5x+4=0$$\Rightarrow (x-1)(x-4)=0$$\Rightarrow x=1,4(>0)$Thus, there is no solution of the equation when $x<0$