Question

已知p:x²+mx+1=0有兩個(gè)不等的負(fù)根,q:4x²+4(m-2)x+1=0無實(shí)根,若p、q一真一假,求m的取值范圍.

Answer 1

解:若p真,則Δ₁=m²-4＞0且m＞0,即m＞2;

若q真,則Δ₂=16(m-2)²-16＜0,即1＜m＜3;

若p真q假,則m＞2且m≤1或m≥3,即m≥3;

若p假q真,則m≤2且1＜m＜3,即1＜m≤2.

綜上,{m|1＜m≤2或m≥3}.