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题库 / OG2017Q-DS-261
In the equation x2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?
(1) x - 3 is a factor of x2 + bx + 12.
(2) 4 is a root of the equation x2 + bx + 12 = 0.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
题目分析：
（1） x-3是~$x^2+bx+12=0$~的一个因子，又因为~$x^2$~的系数为1，所以，设另一个因子为(x+k)，则有(x-3)(x+k)=0，展开得~$x^2+(k-3)x-3k=0$~，有-3k=12，解得k=-4，所以b=k-3=-7。题目得解。
（2）4是~$x^2+bx+12=0$~的一个根，将x=4代入解得b=-7。题目得解。
因此，本题答案为（D），任何一个条件说明均能解题。
4 is a root of the equation x2 + bx + 12 = 0. ---> 4是方程的一个根（一个解）
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