1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Nature of Roots
If a<c<b th...
Question
If
a
<
c
<
b
then the roots of the equation
(
a
−
b
)
2
x
2
+
2
(
a
+
b
−
2
c
)
x
+
1
=
0
are-
A
Imaginary
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
Real
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
One real and one Imaginary
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Equal and Imaginary
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
A
Imaginary
a
<
c
<
b
(
a
−
b
)
2
x
2
+
2
(
a
+
b
−
2
c
)
x
+
1
=
0
△
=
4
(
a
+
b
−
2
c
)
2
−
4
(
a
−
b
)
2
=
4
(
(
a
−
c
)
+
(
b
−
c
)
)
2
−
4
(
(
a
−
c
)
−
(
b
−
c
)
)
2
=
4
(
4
(
a
−
c
)
(
b
−
c
)
)
=
16
(
a
−
c
)
(
b
−
c
)
a
−
c
<
0
&
b
−
c
>
0
(
∵
a
<
c
<
b
)
∴
△
<
0
∴
Roots of given equation are imaginary.
Suggest Corrections
0
Similar questions
Q.
If
a
,
b
,
c
∈
R
+
, then both the roots of the equation
(
x
−
b
)
(
x
−
c
)
+
(
x
−
a
)
(
x
−
c
)
+
(
x
−
a
)
(
x
−
b
)
=
0
are always
Q.
(a) Prove that the roots of
(
a
−
b
)
2
x
2
+
2
(
a
+
b
−
2
c
)
x
+
1
=
0
are real or imaginary according as c does not does lie between a and b,a<b.
(b) If the roots of the equation
(
m
−
3
)
x
2
−
2
m
x
+
5
m
=
0
are real and
+
i
v
e
, then prove that
m
ϵ
]
3
,
15
4
]
(c) If the equation
x
2
+
2
(
a
+
1
)
x
+
9
a
−
5
=
0
has only negative roots, then show that
a
≥
6
.
(d) If both the roots of the equation
x
2
−
6
a
x
+
2
+
2
a
+
9
a
2
=
0
exceed
3
, then show that
a
>
11
9
.
Q.
If
b
1
b
2
=
2
(
c
1
+
c
2
)
and
b
1
,
b
2
,
c
1
,
c
2
are all real numbers, then at least one of the equations
x
2
+
b
1
x
+
c
1
=
0
and
x
2
+
b
2
x
+
c
2
=
0
has
Q.
If the roots of the equation
x
2
−
2
c
x
+
a
b
=
0
are real and unequal, then prove that the roots of
x
2
−
2
(
a
+
b
)
x
+
a
2
+
b
2
+
2
c
2
=
0
will be imaginary.
Q.
If a and b are distinct real numbers, show that the quadratic equation
2
(
a
2
+
b
2
)
x
2
+
2
(
a
+
b
)
x
+
1
=
0
has no real roots.
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Nature and Location of Roots
MATHEMATICS
Watch in App
Explore more
Nature of Roots
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app