If the ratio of ax ^ 2 + BX + C = 0 (a is not equal to 0) is 2:3, then the relationship among a, B and C is Why?

If the ratio of ax ^ 2 + BX + C = 0 (a is not equal to 0) is 2:3, then the relationship among a, B and C is Why?

6b^2=25ac

If the sum of two squares of the quadratic equation AX & # 178; + BX + C = 0 (a ≠ 0) is m, and the sum of two squares is n, then & # 189; an + &# 189; BM + C is equal to?
Expressed by m, n

x1+x2=-b/a=m
(x1+x2)²=b²/a²=m²
x2²+x2²+2x1x2=n+2c/a=m²
an-2c=am²
an=am²+2c
-b=am
bm=-am²
1/2an+1/2bm+c=1/2(am²+2c)-1/2am²+c
=c+c=2c
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Is there something wrong with this question
x²+b/ax+c/a=0
x²-mx+(m²-n)/2=0
Δ=m²-2(m²-n)>=0
-m²>=2n
0

On the image of the quadratic equation AX + 2x-5 = 0 of X

If the binary linear equation AX + 2x-5 = 0 has only one root between 0 and 1 (excluding 0 and 1), find the value range of a, and change the image out. Thank you! Answer: just f (1) > 0

It is known that the quadratic equation of one variable x + ax + A-2 = 0
(1) Verification: no matter a takes any real number, the equation always has two unequal real roots (2). When one root of the equation is - 2, find the other root of the equation

1、
Discriminant = A & # 178; - 4 (A-2)
=(a-2)²+4≥4>0
So there are always two unequal real roots
2、
x=-2
Substituting
4-2a+a-2=0
a=2
x²+2x=0
x(x+2)=0
So the other one is x = 0