Question

填空：如果四個有理數(shù)相乘，積為負數(shù)，那么負因數(shù)個數(shù)是

1或3

．

Answer 1

分析：幾個不為0的數(shù)相乘，積的符號由負因數(shù)的個數(shù)確定，負因數(shù)有奇數(shù)個，積為負；負因數(shù)有偶數(shù)個，積為正．

解答：解：∵abcd＜0，
∴a，b，c，d中有1個或3個負數(shù)，
故答案為：1或3．

點評：本題考查了幾個不等于零的數(shù)相乘，積的符號由負因數(shù)的個數(shù)決定：當負因數(shù)有奇數(shù)個數(shù)，積為負；當負因數(shù)的個數(shù)為偶數(shù)個時，積為正．