二次方程根的分布是竞赛大纲中明确要求的内容,在竞赛中也经常出现.它涉及了有理数、整数、代数式变形等各方面知识,但对知识的要求并不高,解题方法灵活多变,技巧性强,能综合考查参赛者思维的发散性、创造性.它主要有两个方面:一是根据所给方程特点探求根的分布情况;二是由方程根的分布情 The distribution of the roots of the quadratic equation is the content that is explicitly requested in the competition outline. It also appears frequently in competitions. It involves the knowledge of rational numbers, integers, and algebraic deformations, but it does not require high knowledge, and the problem-solving method is much more flexible. Change, strong skills, can comprehensively examine the divergence and creativity of competitor’s thinking. It mainly has two aspects: one is to explore the distribution of the root according to the characteristics of the given equation; the second is the distribution of the root of the equation.