有关方程所有根之和,我们有下列结论:结论1　若函数y =f(x)的图像关于直线x =a对称,且方程f(x) =0有n个根,则这n个根之和为na(n∈N )。证明　y =f(x)的图像关于直线x =a对称 f( 2a -x) =f(x)。令x0 是方程f(x) =0的根,即f(x0 ) =0。代入上式得:f( 2a -x0 ) =f(x0 ) =0 ,所以2a Regarding the sum of all roots of the equation, we have the following conclusions: Conclusion 1 If the image of the function y = f(x) is symmetrical about the straight line x = a, and the equation f(x) =0 has n roots, then the n roots And for na(n∈N). Prove that the image of y = f(x) is symmetrical about the line x = a f(2a - x) = f(x). Let x0 be the root of the equation f(x) = 0, that is, f(x0) = 0. Substituting into the above formula: f( 2a -x0 )=f(x0 )=0, so 2a