一元二次方程的根与系数关系,通常也称韦达定理,是由十六世纪法国最杰出的数学家韦达发现的。定理:设方程ax~2+bx+c=0(a≠0)的两根为x_1、x_2,那么x_1+x_2=-b/a,x_1x_2=c/a。根与系数关系中包含了丰富的数学内容,应用非常广泛,在代数、几何中经常用到,主要体现在以下几个方面。1运用根与系数关系,求方程中参数的值例1已知关于x的方程x~2+4x+a=0,且 The root-coefficient relationship of the quadratic equation, often called the Vedic theorem, was discovered by Vedic, the most prominent mathematician in France in the 16th century. Theorem: Let two equations of ax 2 + bx + c = 0 (a ≠ 0) be x_1, x_2, then x_1 + x_2 = -b / a, x_1x_2 = c / a. The relationship between roots and coefficients contains a wealth of mathematical content, is widely used in algebra, geometry often used, mainly in the following areas. 1 Use the relationship between roots and coefficients to find the values ​​of the parameters in the equation Example 1 Known x for equations x ~ 2 + 4x + a = 0, and