小明经常遇到这样的一元二次方程x2+3x+2=0,5x2-7x+2=0,….发现它们总有一个根为1,这是否成一个规律呢? 猜想1 方程ax2+bx+c=0(a≠0)中,若有a+b+c=0则方程有一个根为1,另一个根是常数项与二次项系数的比. 小芳对于小明提出的猜想很感兴趣,连忙对小明说:①求证方程(a-b)x2+(b-c)x+c-a=0(其中a≠b)有一个根是1.②若x=1是方程ax2+bx+c=0的根,则 Xiao Ming often encounters such a quadratic equation x2+3x+2=0, 5x2-7x+2=0, .... It is found that they always have a root of 1, is this a rule? Conjecture 1 Equation ax2+bx In +c=0(a≠0), if there is a+b+c=0, the equation has a root of 1, and the other root is the ratio of the constant term to the coefficient of the quadratic term. Xiaofang’s conjecture for Xiaoming is very Interested, quickly said to Xiao Ming: 1 to verify the equation (ab) x2 + (bc) x + ca = 0 (where a ≠ b) has a root is 1.2 if x = 1 is the equation ax2 + bx + c = 0 Root, then