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:
x−2=4−x,x−2=16−8x+x2,
0=x2−9x+18=(x−6)(x−3);∴x=6,x=3.
A check is obtained only with x=3.