Problem: The symbol β£xβ£ means x if x is not negative and βx if x is not positive. We may then say concerning the solution of β£xβ£2+β£xβ£β6=0 that:
Answer Choices:
A. there is only one root
B. the sum of the roots is +1
C. the sum of the roots is 0
D. the product of the roots is +4
E. the product of the roots is -6
Solution:
If x>0x2+xβ6(xβ2)(x+3)β=0=0βx+3ξ =0x=2
If x<0,x2βxβ6(xβ3)(x+2)β=0=0βxβ3ξ =0,x=β2
or
[β£xβ£+3][β£xβ£β2]=0β£xβ£+3ξ =0 thereforeβ£xβ£=2, i.e., x=2 or β2