How many root does this equation have? and what type is it ?
X² - 3X + 7 = 0

The equation is of the form
a
x
2
+
b
x
+
c
=
0
where:
a
=
1
,
b
=
−
3
,
c
=
−
7
The Discriminant is given by:
Δ
=
b
2
−
4
⋅
a
⋅
c

=
(
−
3
)
2
−
(
4
⋅
1
⋅
−
7
)

=
9
+
28
=
37
The solutions are found using the formula
x
=
−
b
±
√
Δ
2
⋅
a
x
=
−
(
−
3
)
±
√
37
2
⋅
1
=
3
±
√
37
2
The solutions are
x
=
3
+
√
37
2
x
=
3
−
√
37
2