3x^2 +2x-7=0 solve by formula method
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Answer:
Our equation is of the form
a
x
2
+
b
x
+
c
=
0
, therefore, we can use the quadratic formula. The quadratic formula is
x
=
−
b
±
√
D
2
a
, with
D
=
b
2
−
4
a
c
. We see that
a
=
3
,
b
=
−
2
and
c
=
7
.
Firstly, we calculate
D
.
D
=
b
2
−
4
a
c
=
(
−
2
)
2
−
4
⋅
3
⋅
7
=
−
80
. Because D is less than zero, there are no real roots. We can however calculate the imaginary solutions. We just calculate
x
:
x
=
−
b
±
√
D
2
a
=
2
±
√
−
80
2
⋅
3
=
2
±
√
−
1
⋅
√
16
⋅
√
5
6
=
2
±
i
⋅
4
√
5
6
=
1
3
±
2
3
i
√
5
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