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定理1:若二次函数y=ax~2+bx+c[a≠0]图象与x轴的两个交点在坐标原点的同侧,则必有对应的二次方程ax~2+bx+c=0[a≠0]的{△>0 (x_1x_1)>0}(x_1,x_2 为方程ax~2+bx+c=0[a≠0]的两根)。反之亦然。 证明:∵ 二次函数的y=ax~2+bx+c[a≠0]的图象与x轴有两个交点 ∴ ax~2+bx+c=0有两个不等的实根
Theorem 1: If the quadratic function y = ax ~ 2 + bx + c [a ≠ 0] The two points of intersection between the image and the x axis are on the same side of the coordinate origin, then there must be a corresponding quadratic equation ax ~ 2 + bx {△> 0 (x_1x_1)> 0} (x_1, x_2 for two equations with ax = 2 + bx + c = 0 [a ≠ 0]) for + c = 0 [a ≠ 0]. vice versa. It is proved that the image of y = ax ~ 2 + bx + c [a ≠ 0] of ∵ quadratic function has two intersections with the x axis ∴ ax ~ 2 + bx + c = 0 There are two unequal real roots