Find the roots of the following quadratic equations by factorisation:
i x2– 2x – 9 = 0
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Answer:
In the equation
x
2
−
2
x
+
9
=
0
, the coefficients are rational but as the discriminant is
(
−
2
)
2
−
4
×
1
×
9
=
4
−
36
=
−
32
is negative, the roots of the equation are pair of complex conjugate numbers. Hence, we can use quadratic formula to get roots.
Quadratic formula gives the roots of
a
x
2
+
b
x
+
c
=
0
as
x
=
−
b
±
√
b
2
−
4
a
c
2
a
. Note that
b
2
−
4
a
c
is the discriminant.
Hence solution of
x
2
−
2
x
+
9
=
0
is given by
x
=
−
(
−
2
)
±
√
(
−
2
)
2
−
4
×
1
×
9
2
×
1
or
x
=
2
±
√
−
32
2
i.e.
x
=
2
+
i
4
√
2
2
or
x
=
2
−
i
4
√
2
2
i.e.
x
=
1
+
i
2
√
2
or
x
=
1
−
i
2
√
2
Step-by-step explanation:
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