若A={x丨x²+px+q=0,x∈R},B={x丨x²-3x+2=0,x∈R},A∪B=B,求p,q应满足的条件!

题目

若A={x丨x²+px+q=0,x∈R},B={x丨x²-3x+2=0,x∈R},A∪B=B,求p,q应满足的条件!

答案

B={x丨x²-3x+2=0,x∈R}则 B={x丨（x-1）（x-2）=0,x∈R}B={x=1,x=2}A∪B=B则A∈BA={x=1},A={x=2},A={x=1,x=2}1)当A={x=1}1²+p+q=0 p+q=-12)当A={x=3}4+2p+q=0 2p+q=-43) 当A={x=1,x=2}1+p+q=0 （1）4+2p+q...