在什么条件下,一元二次方程的根才是整数呢?下面几个定理部分回答了这个问题. 定理1 若首项系数为1的整系数方程x2+px+q=0(p、q为整数)的判别式Δ=p2-4q为一个完全平方数,则方程的根为整数.反之,亦成立. 这个定理可用反证法来证明,这里从略.只强调一点:对首项系数不 Under what conditions, is the root of the quadratic equation of quadratic equations an integer? The following theorems partially answer this question. Theorem 1 If the first coefficient of the integral coefficient is x + px + q = 0 (p, q is If the discriminant Δ=p2-4q of the integer is a complete square, then the root of the equation is an integer. Conversely, it is true. This theorem can be proved by the anti-evidence method. Here we will only emphasize one point: the first coefficient is not