解:(1)
a=2,b=3,c=-4,
∵
=
∴方程有兩個(gè)不相等的實(shí)數(shù)根.
(2)將方程化為一般形式

a=3, ,c=2
∵

∴方程有兩個(gè)相等的實(shí)數(shù)根.
(3)將方程化為一般形式

方程兩邊同乘以2(為了計(jì)算簡(jiǎn)便),得

, ,c=2
∵

∴方程沒(méi)有實(shí)數(shù)根.
(4)
∵a≠0,∴方程是一元二次方程,
此方程是缺少常數(shù)項(xiàng)的不完全的一元二次方程,可將常數(shù)項(xiàng)視為零.
∵
∵無(wú)論b取任何實(shí)數(shù), 均為非負(fù)數(shù),
∴Δ≥0,
故方程有兩個(gè)實(shí)數(shù)根.
(5)
∵a≠0,
∴此方程是缺少一次項(xiàng)的不完全的一元二次方程,一次項(xiàng)系數(shù)6=0.
∵
=-4ac
需要討論a,c的符號(hào),才能確定Δ的符號(hào);
當(dāng)c=0時(shí),Δ=0,方程有兩相等實(shí)根;
當(dāng)a與c異號(hào)時(shí),Δ>0,方程有兩不等實(shí)根;
當(dāng)a與c同號(hào)時(shí),Δ<0,方程沒(méi)有實(shí)數(shù)根.
|