1.x²-3x+2-m²=0
∵Δ=b²－4ac
=(-3) ²－4×1×(2-m²)
=9-8+4m²
=4m²+1＞1＞0
∴方程有两个不相等的实数根.
2.x²-3x+m²+3=0
∵Δ=b²－4ac
=(-3) ²－4×1×(m²+3)
=9－4m²－12
=-4m²－3≤-3＜0
∴方程没有实数根.
3.x²-（m+1）x+m=0.
∵Δ=b²－4ac
=[-(m+1) ]²－4×1×m
=m²+2m+1－4m
=m²-2m+1
=(m-1) ²≥0
∴方程有实数根.
4.x²+（m+2）x-（3m+20）=0
∵Δ=b²－4ac
=(m+2) ²－4×1×[-(3m+20)]
=m²+4m+4+12m+80
=m²+16m+84
=( m²+16m+64)+20
=(m+8) ²+20≥20＞0
∴方程有两个不相等的实数根.