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高一代数在第一学期讲的內容是冪和方根,二次方程和可化为二次方程的方程。本文打算提出有关复习二次方程的一些問題。 (一)关于解一元二次方程教师应着重要求学生,对于二次方程,不但要会正确地解,而且会用简捷的方法去解,并能达到熟练程度。 1.如果所給的二次方程能写成特殊形状 ax~2+c=0,ax~2+bx=0就直接求出它們的根,不必应用二次方程求根公式来解。 2.如果所給的二次方程很容易利用视察法来求出它的一个根,那末就可以利用韦达定理求它的另一个根。例如解方程 (a-b)x~2+(b-c)x+(c-a)=0(a≠b),由視察,设x=1得 (a-b)+(b-c)+(c-a)=0,
The contents of the first generation in the first generation are the power and square roots, quadratic equations, and equations that can be converted to quadratic equations. This article intends to raise some questions regarding the review of quadratic equations. (A) The teacher who solves the quadratic equation should pay attention to the students. For the quadratic equation, not only will it be solved correctly, but also it will be solved in a simple and straightforward way and it can reach the level of proficiency. 1. If the given quadratic equation can be written as a special shape ax~2+c=0 and ax~2+bx=0, their roots can be found directly. It is not necessary to use the quadratic equation to solve the root formula. 2. If the given quadratic equation easily finds one of its roots using the inspection method, then we can use Vedic’s theorem to find another root of it. For example, solving the equation (a-b) x~2+(b-c)x+(c-a)=0(a≠b), from the inspection, let x=1 be (a-b)+(b-c)+(c-a)=0,