For the values of x is the expression 2x2+9x+10positive
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Given:
2
x
2
+
9
x
+
10
=
0
We can use an AC method.
Find a pair of factors of
A
C
=
2
⋅
10
=
20
with sum
B
=
9
The pair
5
,
4
works.
Use this pair to split the middle term and factor by grouping:
0
=
2
x
2
+
9
x
+
10
0
=
2
x
2
+
5
x
+
4
x
+
10
0
=
(
2
x
2
+
5
x
)
+
(
4
x
+
10
)
0
=
x
(
2
x
+
5
)
+
2
(
2
x
+
5
)
0
=
(
x
+
2
)
(
2
x
+
5
)
Hence solutions:
x
=
−
2
or
x
=
−
5
2
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