先看看判别式.4nn-4mq=4(nn-mq)=4[(DC+CN)(DC+CN)-(BD+DC+CN)CN]
=4[DC·DC+2DC·CN+CN·CN-BD·CN-DC·CN-CN·CN]=4[DC·DC+2DC·CN-BD·CN-DC·CN]
=4[DC·DC+DC·CN-BD·CN]=4[DC·DC+(DC·CN-BD·CN)]=4[DC·DC-(BD-DC)·CN]
∵BD/DC=(BC+2CN)/(2CN)=BC/(2CN)+1,BC/(2CN)=BD/DC-1=(BD-DC)/DC,CN=BC·DC/[2(BD-DC)]=(BD+DC)DC/[2(BD-DC)],∴4nn-4mq=4[DC·DC-(BD-DC)·CN]=4{DC·DC-(BD-DC) (BD+DC)DC/[2(BD-DC)] }=4{DC·DC- (BD+DC)DC/2}=4DC(2DC-BD-DC)/2=2DC(DC-BD).又∵DC＜BD,∴2DC(DC-BD)＜0,即4nn-4mq＜0,∴mxx-2nx+q=0无实数根.
（请你仔细检查一下上面的过程或举一个具体例子检查一下这个结果）