Question

一元二次方程a(x-1)平方+b(x-1)+c=0化为一般形式后为2x平方-3x-1=0，则(a+b)÷c的值为?

Answer 1

a(x-1)平方+b(x-1)+c=0
a(x-1)^2+b(x-1)+c=0
ax^2+(b-2a)x+a-b+c=0
a=2
b-2a=-3
a-b+c=-1

b=1
c=-2

(a+b)/c=-3/2

Answer 2

a(x-1)平方+b(x-1)+c=0
(x1-1)+(x2-1)=-b/a, ==> x1+x2=-(b/a)+2
(x1-1)*(x2-1)=c/a, ==> x1*x2-(x1+x2)+1=c/a

而：x1+x2=3/2
x1*x2=-1/2

所以：3/2=-(b/a)+2
(-1/2)-(3/2)+1=c/a

b=(1/2)a
c=-a

(a+b)÷c=[1+(1/2)]/(-1)=-3/2

Answer 3

a=2 b=1 c=-2
答案 -3/2

Answer 4

a(x-1)^2+b(x-1)+c=0
ax^2-2ax+a^2+bx-b+c=0
所以
a=2
-2a+b=-3
a-b+c=0
解得
b=1
c=-2

（a+b）/c=-3/2