3x²+7x+4=0 . solve by factorization method Answer me &Get points ☺️☺️☺️
Answers
Answer:
-4/3
Step-by-step explanation:
Quick Method
Notice that if you invert the sign of the term of odd degree then the sum of the coefficients is zero. That is: 3−7+4=0
We can deduce that x=−1 is a root and (x+1) a factor:
0=3x2+7x+4=(x+1)(3x+4)
So the other root is x=−4/3
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Answer:
Notice that if you invert the sign of the term of odd degree then the sum of the coefficients is zero. That is:
3
−
7
+
4
=
0
We can deduce that
x
=
−
1
is a root and
(
x
+
1
)
a factor:
0
=
3
x
2
+
7
x
+
4
=
(
x
+
1
)
(
3
x
+
4
)
So the other root is
x
=
−
4
3
AC Method
Look for a pair of factors of
A
C
=
3
⋅
4
=
12
with sum
B
=
7
.
The pair
3
,
4
works.
Use that pair to split the middle term and factor by grouping:
0
=
3
x
2
+
7
x
+
4
=
3
x
2
+
3
x
+
4
x
+
4
=
(
3
x
2
+
3
x
)
+
(
4
x
+
4
)
=
3
x
(
x
+
1
)
+
4
(
x
+
1
)
=
(
3
x
+
4
)
(
x
+
1
)
Hence roots
x
=
−
4
3
and
x
=
−
1
Completing the square
Use the difference of squares identity too:
a
2
−
b
2
=
(
a
−
b
)
(
a
+
b
)
with
a
=
(
6
x
+
7
)
and
b
=
1
First multiply the equation by
2
2
⋅
3
=
12
to cut down on the fractions involved:
0
=
3
x
2
+
7
x
+
4
becomes
0
=
36
x
2
+
84
x
+
48
=
(
6
x
+
7
)
2
−
49
+
48
=
(
6
x
+
7
)
2
−
1
2
=
(
(
6
x
+
7
)
−
1
)
(
(
6
x
+
7
)
+
1
)
=
(
6
x
+
6
)
(
6
x
+
8
)
=
(
6
(
x
+
1
)
)
(
2
(
3
x
+
4
)
)
=
12
(
x
+
1
)
(
3
x
+
4
)
Hence roots
x
=
−
1
and
x
=
−
4
3
Step-by-step explanation: