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实系数一元二次方程ax~2+bx+c=0(其中a≠0)的判别式Δ=b~2-4ac,与方程的根,有下列关系存在: >0时,方程有两个不等的实根; Δ=b~2-4ac =0时,方程有两个相等的实根; <0时,方程没有实根。从几何意义上来看,二次函数y=ax~2+bx+c(其中a≠0)的图象是一条抛物线,也有下列关系存在: >0时,抛物线与x轴有两个交点(相交); Δ=b~2-4ac =0时,抛物线与x轴有一个交点(相切); <0时,抛物线与x轴没有交点(相离)。
The discriminant Δ=b~2-4ac of the real coefficient quadratic equation ax~2+bx+c=0 (where a ≠ 0), and the root of the equation, has the following relationship: When >0, the equation has two Unequal real roots; When Δ=b~2-4ac =0, the equation has two equal real roots; <0, the equation has no real roots. From a geometrical point of view, the image of the quadratic function y=ax~2+bx+c (where a ≠ 0) is a parabola, and the following relationship exists: When >0, the parabola has two intersections with the x axis (intersection ); Δ=b~2-4ac =0, the parabola has an intersection with the x-axis (tangent); <0, the parabola has no intersection with the x-axis (away).