定理　一元二次方程ax2 +bx+c=0 (a≠ 0 )有一个根为 1的充要条件是a+b+c=0 .这个定理的形式很简单 ,证明很容易(略 ) ,应用也很方便 .1　求根例 1　 (第五届初中“祖冲之杯”赛试题 )若a为正数 ,那么方程 (2a+3)x2 +(a+2 )x- (3a+5) =0的两根中较大的一个实根是 .解　因为 (2a Theorem The quadratic equation ax2 + bx + c = 0 (a ≠ 0) has a root 1 with a sufficient and necessary condition that a + b + c = 0. The form of this theorem is very simple, it is easy to prove (slightly), application It is also very convenient.1 Root 1 (the 5th junior high school “Zu Chong Cup” test) If a is positive, then the equation (2a+3)x2+(a+2)x-(3a+5)=0 The larger of the two roots is the root solution. Solution because (2a