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人教版初中《代数》第三册给出了一个重要的代数恒等式:ax2+bx+c=a(x-x1)(x-x2),其中x1,x2是二次方程ax2+bx+c=0的两个根,也是二次函数y=ax2+bx+c与x轴两个交点的横坐标.巧妙地运用这一恒等式解题可使解题思路明显,过程简捷.下面以若干竞赛题为例说明这一恒等式的应用.
An important algebraic identity is given in the third edition of the Algebra of the junior high school teaching journal: ax2+bx+c=a(x-x1)(x-x2), where x1,x2 is the quadratic equation ax2+bx+c The two roots of =0 are also the abscissas of the intersection point of the quadratic function y=ax2+bx+c and the x-axis. Cleverly applying this identity problem solving makes the problem-solving idea obvious and the process simple. The following are some contests. Examples illustrate the application of this identity.