if x^2-(5m-2)x+4m^2 +10m+25=0 were to be a perfect square then m=
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x² -(5m -2)x + 4m² + 10m +25 = 0
this is perfect square it means
D = 0 then, this will be possible
so,
D = b² -4ac = (5m -2)² -4(4m²+10m+25)=0
25m² +4 -20m -16m² -40m -100 = 0
9m² -60m -96 = 0
3m² -20m -32 = 0
m = { 20±√(400+384)}/6
= { 20±√784}/6
={ 20±28)/6
=8, -4/3
this is perfect square it means
D = 0 then, this will be possible
so,
D = b² -4ac = (5m -2)² -4(4m²+10m+25)=0
25m² +4 -20m -16m² -40m -100 = 0
9m² -60m -96 = 0
3m² -20m -32 = 0
m = { 20±√(400+384)}/6
= { 20±√784}/6
={ 20±28)/6
=8, -4/3
Ramu111:
so talented bro
:-)
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