Question

不等式(x^2-ax+b)/(x^2-cx+d)≥0的解集为(-∞,-1]∪（1,2]∪(3,+∞),求向量m=(a,b

Answer 1

根据解集的形式,能取到区间端点的为分子方程的解.

因此,x^2-ax+b = (x+1)(x-2) = x^2 - x - 2

所以 a =1,b = -2

而 x^2-cx+d = (x-1)(x-3) = x^2 - 4x + 3

所以 c = 4,d = 3

m与n的向量积为 1×4 + (-2)×3 = -2