一元二次方程的根与系数的关系,即韦达定理,是初中数学中一个充满活力的定理,应用极为广泛.本文以1996、1997两年全国各地中考试题为例,介绍它的应用. 一、求一元二次方程根的对称式的值若x_1、x_2是方程ax~2+bx+c=0(a≠0)的两个实数根,应用韦达定理,可不解方程直接求得x_ The relationship between the root and the coefficient of the quadratic equation, ie, Weida’s theorem, is a dynamic theorem in junior middle school mathematics. It is widely used. This article takes the middle school exams in the country in 1996 and 1997 as an example to introduce its application. Solve the symmetry of the root of a quadratic equation If x_1, x_2 are the two real roots of the equation ax~2+bx+c=0(a≠0), use the Weddah’s theorem to solve the equation directly and obtain x_