ax^2+bx+c=0 If the ratio of the two seeds in this equation is 3: 4, it proves that 12 b ^ 2 = 49 a c
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Answer:
Step-by-step explanation:
12
b
2
=
49
a
c
Explanation:
y
=
a
x
2
+
b
x
+
c
=
0
Reminder of the improved quadratic formula (Socratic Search)
Determinant -->
D
=
d
2
=
b
2
−
4
a
c
, with
d
=
±
√
D
The 2 real roots are:
x
=
−
b
2
a
±
d
2
a
x
1
=
−
b
+
d
2
a
x
2
=
−
b
−
d
2
a
=
−
(
b
+
d
)
2
a
The ration
x
1
x
2
=
3
4
=
d
−
b
−
(
b
+
d
)
Cross multiply -->
- 3b - 3d = 4d - 4b
4b - 3b = 4d + 3d
b = 7d.
Square both sides -->
b
2
=
49
d
2
=
49
(
b
2
−
4
a
c
)
=
49
b
2
−
196
a
c
48
b
2
=
196
a
c
. Simplify by 4.
12
b
2
=
49
a
c
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