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在判别式Δ=b2-4ac≥0的条件下,一元二次方程ax2+bx+c=0(a≠0)有两个实根x1、x2,x1、x2与数轴上点X1、X2对应,设实数m、n、p、q与数轴上的点M、N、P、Q对应,点X1、X2相对于M、N、P、Q中的某些点(称作界点)所处的位置状态,称为点X1、X2的分布,对应称为一元二次方程实根的分布.实根x1、x2的分布在数量上表现为x1、x2与m、n、…间的大小关系(或用元素x1、x2与区间的关系表示).由于二次方程根公式中含b2槡-4ac,则一元二次方程实根的分布问题通常化归为无理不等式处理(繁琐),或结合二次函数图象考虑对称轴位置和界点处函数值正负,转化为不等式组处理.下面介绍
Under the condition of discriminant Δ = b2-4ac≥0, the quadratic equation ax2 + bx + c = 0 (a ≠ 0) has two real roots x1, x2, x1, x2 corresponding to the points X1 and X2 Let the real numbers m, n, p, q correspond to the points M, N, P, Q on the number axis, and the points X1, X2 relative to some points in M, N, P, Q Is called the distribution of points X1 and X2, and is correspondingly called the distribution of real roots of the quadratic equation. The distribution of real roots x1 and x2 is quantitatively expressed as the size relationship between x1, x2 and m, n, ... (Or the relationship between the elements x1, x2 and the interval) .Because the equation of the quadratic root contains b2 槡 -4ac, the distribution of real roots of the quadratic equation is generally classified as irrational inequality (tedious), or combined Quadratic function image considering the symmetry axis position and the function of the value at the point of positive and negative, converted to inequality group processing.