x1=(-b+√(b^2-4ac))/(2a),x2=(-b+√(b^2-4ac))/(2a)
=>x1+x2=-2b/(2a)=-b/a
x1x2=(-b+√(b^2-4ac))(-b-√(b^2-4ac))/(2a)^2=(b^2-(b^2-4ac))/(4a^2)=c/a
采用求根公式太复杂,如果用待定系数法则很简单,而且很容易推广到n次方程
a(x-x1)(x-x2)
=ax^2-a(x1+x2)x+ax1x2
=ax^2+bx+c
由系数对应得到:
-a(x1+x2)=b
ax1x2=c
所以:x1+x2=-b/a,x1x2=c/a
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