由求根公式
x1=[-b-√(b²-4ac)]/2a
x2=[-b+√(b²-4ac)]/2a
所以
x1+x2
=[-b-√(b²-4ac)]/2a+[-b+√(b²-4ac)]/2a
=[-b-√(b²-4ac)-b+√(b²-4ac)]/2a
=-2b/2a
=-b/a
x1x2
=[-b+√(b²-4ac)]/2a*[-b+√(b²-4ac)]/2a
由平方差
=[b²-(b²-4ac)]/(4a)²
=4ac/(4a²)
=c/a
由求根公式
x1=[-b-√(b²-4ac)]/2a
x2=[-b+√(b²-4ac)]/2a
所以
x1+x2
=[-b-√(b²-4ac)]/2a+[-b+√(b²-4ac)]/2a
=[-b-√(b²-4ac)-b+√(b²-4ac)]/2a
=-2b/2a
=-b/a
x1x2
=[-b+√(b²-4ac)]/2a*[-b+√(b²-4ac)]/2a
由平方差
=[b²-(b²-4ac)]/(4a)²
=4ac/(4a²)
=c/a