根据题意有: x^2 - 2x + k = (x + 1/3)( x + b)
由于( x + 1/3)( x + b) = x^2 + bx + (1/3)x + (1/3)b
= x^2 + (b + 1/3)x + (1/3)b
所以有: x^2 - 2x + k = x^2 + (b + 1/3)x + (1/3)b
比较上式两边可得: b + 1/3 = - 2 (1)
k = (1/3)b (2)
解(1)得: b = - 7/3 (3)
把(3)代入(2)得: k = (1/3)×(-7/3) = -7/9