Problem: The symbol ∣x∣ means x if x is not negative and −x if x is not positive. We may then say concerning the solution of ∣x∣2+∣x∣−6=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+x−6(x−2)(x+3)​=0=0​x+3î€ =0x=2
If x<0,x2−x−6(x−3)(x+2)​=0=0​x−3î€ =0,x=−2
or
[∣x∣+3][∣x∣−2]=0∣x∣+3î€ =0 therefore∣x∣=2, i.e., x=2 or −2