Thinking: This is the application of Vieta's theorem.

1,

(1) Let two be x 1, x2.

x 1+x2=- 1

x 1-x2= 1

Solution: x 1=0, x2=- 1.

(2)x 1+x2 =-b/(a+c)=- 1

x 1*x2=(a-2c)/(a+c)=0

Solution:

a=2c

b=3c

Therefore, A: B: C = 2: 3: 1.

2, because A just misread the coefficient of the quadratic term, so it can be assumed that he regards the coefficient of the quadratic term as m, then

According to Vieta theorem

-b/m=5

c/m=4

Solution: b=-5m

c=4m

Student B mispronounced the signs of the linear term coefficient and the constant term. We assume that he regards the linear term coefficient as n and the constant term as -c, and from Vieta's theorem, we get:

-c/a=- 12

So:

a:b:c = 1:- 15: 12

The original equation obtained by bringing it into the equation is:

x^2- 15x+ 12=0