§1.前言 現行高中代数第一册“根据判別式和系数討論完全二次方程”一节里,对于簡化完全二次方程x~2+2px+q=0可用分析方法討論得出下列結果。 (Ⅰ)当Δ=p~2-q<0时,沒有实数根。 (Ⅱ)当Δ=p~2-q=0时,有两个相等的实数根。 (Ⅲ)当Δ=p~2-q<0时,有两个不等的实数根。 (ⅰ)如q>0,两根同号。当p>0,两根都是負数; p<0,两根都是正数。 (ⅱ)如q<0,两根异号。当p>0,負数根的絕对值大; p<0,正数根的絕对值大。在这以前,学生学习了韦达定理,在这以后学生又 §1. Foreword In the section entitled “Comprehensive quadratic equations based on discriminants and coefficients” in the current Senior High School Algebra Volume 1, the following results are discussed for the simplified full quadratic equation x~2+2px+q=0. (I) When Δ=p~2-q<0, there is no real number root. (II) When Δ=p~2-q=0, there are two equal real roots. (III) When Δ=p~2-q<0, there are two unequal real roots. (i) If q>0, two identical numbers. When p>0, both are negative; p<0, both are positive. (ii) If q<0, two different signs. When p>0, the absolute value of the negative root is large; p<0, the positive value of the positive root is large. Before this, students learned the Vedic theorem, after which the students again