代数二次方程讨论的基本理论是判别式定理与韦达定理,定理所叙述的条件对于方程的根来说都是充分而又必要的。但由于方程讨论时缺乏几何证明中的那种严谨性,所以有时常常忽略了条件的正确运用,有时又混淆了条件的必要性与充分性,而导致谬误。下面举例说明解法中常见到的一些错误。 例1.k为何值时,x的二次方程 The basic theories discussed in algebraic quadratic equations are the discriminant theorem and Vedic theorem. The conditions described by the theorem are both sufficient and necessary for the root of the equation. However, due to the lack of strictness in the geometric proofs when discussing the equations, the correct use of conditions is sometimes overlooked, and sometimes the necessity and adequacy of the conditions are confused, leading to errors. The following examples illustrate some of the common mistakes in the solution. Example 1. The quadratic equation of x when the value of k is