Problem:
The equation x+x−2=4 has:
Answer Choices:
A. 2 real roots
B. 1 real and 1 imaginary root
C. 2 imaginary roots
D. no roots
E. 1 real root and 1 extraneous root
Solution:
Solving the equation:
x−2x−2x−200∴x=4−x=(4−x)2=16−8x+x2=x2−9x+18=(x−6)(x−3)=6 or x=3
A check of the solutions shows that only x=3 is valid, as x=6 is an extraneous root.
Answer: E.