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一元二次方程ax2+bx+c=0(a≠0)根的分布问题,实质上是函数 f(x)=ax2+bx+c(a≠0)的零点分布问题,即抛物线与x轴的交点问题．下面从两个视角审视一元二次方程根的分布问题:(1)方程视角(韦达定理法);(2)函数视角(图象法)．设一元二次方程ax2+bx+c=0(a≠ 0)的两根为x1、x2,m、n、p、q∈R,则有:
The problem of the distribution of the quadratic equation ax2+bx+c=0(a≠0) is essentially the zero distribution of the function f(x)=ax2+bx+c(a≠0), that is, the parabola and the x-axis. The intersection problem. The following examines the distribution of the roots of the univariate quadratic equations from two perspectives: (1) the equation perspective (Weidad theorem); (2) the functional perspective (image method). Let two of the quadratic equation ax2+bx+c=0(a≠ 0) be x1,x2,m,n,p,q∈R, then there are: