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Byju's Answer
Standard IX
Mathematics
Factor Theorem
If a and ...
Question
If
a
and
b
are real and
(
i
4
+
3
i
)
a
+
(
i
−
1
)
b
+
5
i
3
=
0
, find
a
and
b
.
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Solution
(
i
4
+
3
i
)
a
+
(
i
−
1
)
b
+
5
i
3
=
0
(
1
+
3
i
)
a
+
(
i
−
1
)
b
−
5
i
=
0
a
+
3
a
i
+
b
i
−
b
−
5
i
=
0
(
a
−
b
)
+
(
3
a
+
b
−
5
)
i
=
0
a
−
b
=
0
.....(i)
b
=
a
3
a
+
b
−
5
=
0
3
a
+
a
−
5
=
0
4
a
=
5
a
=
5
4
a
=
b
=
5
4
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0
Similar questions
Q.
If
a
and
b
are real and
3
+
i
is a root of
x
2
+
a
x
+
b
=
0
, then
a
is
Q.
I: If
a
,
b
,
c
are real, the roots of
(
b
−
c
)
x
2
+
(
c
−
a
)
x
+
(
a
−
b
)
=
0
are real and equal, then
a
,
b
,
c
are in A.P.
II: If
a
,
b
,
c
are real and the roots of
(
a
2
+
b
2
)
x
2
−
2
b
(
a
+
c
)
x
+
b
2
+
c
2
=
0
are real and equal, then
a
,
b
,
c
are in H.P.
Which of the above statement(s) is(are) true?
Q.
If a and b are real numbers between 0 & 1 such that the points
z
1
=
a
+
i
,
z
2
=
1
+
b
i
&
z
3
=
0
form an equilateral triangle, then find
a
and
b
Q.
If
f
(
a
+
b
+
1
−
x
)
=
f
(
x
)
∀
x
, where
a
and
b
are fixed positive real numbers, then
1
(
a
+
b
)
b
∫
a
x
(
f
(
x
)
+
f
(
x
+
1
)
)
d
x
is equal to
Q.
If
a
and
b
are real numbers between
0
and
1
such that the points
z
1
=
a
+
i
,
z
2
=
1
+
b
i
and
z
3
=
0
from an equilateral triangle, then find the values of
′
a
′
and
′
b
′
.
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