the zero of the quadratic polynomial 3 x square +5x+12 are positive or negative
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0
Answer:
or
x
=
−
4
3
Explanation:
Method 1 - Completing the square
0
=
12
(
3
x
2
−
5
x
−
12
)
0
=
36
x
2
−
60
x
−
144
0
=
(
6
x
)
2
−
2
(
6
x
)
(
5
)
+
25
−
169
0
=
(
6
x
−
5
)
2
−
13
2
0
=
(
(
6
x
−
5
)
−
13
)
(
(
6
x
−
5
)
+
13
)
0
=
(
6
x
−
18
)
(
6
x
+
8
)
0
=
(
6
(
x
−
3
)
)
(
2
(
3
x
+
4
)
)
0
=
12
(
x
−
3
)
(
3
x
+
4
)
Hence:
x
=
3
or
x
=
−
4
3
Method 2 - AC method
Given:
3
x
2
−
5
x
−
12
Find a pair of factors of
A
C
=
3
⋅
12
=
36
which differ by
B
=
5
The pair
9
,
4
works.
Use this pair to split the middle term, then factor by grouping:
0
=
3
x
2
−
5
x
−
12
0
=
(
3
x
2
−
9
x
)
+
(
4
x
−
12
)
0
=
3
x
(
x
−
3
)
+
4
(
x
−
3
)
0
=
(
3
x
+
4
)
(
x
−
3
)
Hence:
x
=
−
4
3
or
x
=
3
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