已知命题P：方程x^2+mx+1=0有两个不相等的负数根,命题Q：方程4x^2+4(m-2)x+1=0无实根,若“p或q”为真,"p且q"为假,求实数m的取值范围

Question

已知命题P：方程x^2+mx+1=0有两个不相等的负数根,命题Q：方程4x^2+4(m-2)x+1=0无实根,若“p或q”为真,
"p且q"为假,求实数m的取值范围

Answer 1

已知命题P：方程x^2+mx+1=0有两个不相等的负数根,命题Q：方程4x^2+4(m-2)x+1=0无实根,若“p或q”为真,"p且q"为假,求实数m的取值范围
若“p或q”为真,"p且q"为假,
则需分两种情况讨论:
1.命题Q：方程4x^2+4(m-2)x+1=0无实根,为真,
命题P：方程x^2+mx+1=0有两个不相等的负数根,为假;
命题Q：方程4x^2+4(m-2)x+1=0无实根,为真时,
命题P：方程x^2+mx+1=0有两个不相等的负数根,显然为假;
即:方程4x^2+4(m-2)x+1=0无实根
方程4x^2+4(m-2)x+1=0无实根
有△=[4(m-2)^2]-4*4*1