1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard X
Mathematics
Nature of Roots
Roots of 12...
Question
Roots of
1
2
x
2
+
(
a
+
b
+
c
)
x
+
a
b
+
b
c
+
c
a
=
0
are
A
imaginary
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
real and distinct
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
equal
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
none
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
C
real and distinct
Here
a
=
1
2
,
b
=
a
+
b
+
c
,
c
=
a
b
+
b
c
+
c
a
For Nature of Roots, we need to calculate
b
2
−
4
a
c
⟹
(
a
+
b
+
c
)
2
−
4
(
1
2
)
(
a
b
+
b
c
+
c
a
)
⟹
a
2
+
b
2
+
c
2
+
2
a
b
+
2
b
c
+
2
c
a
−
2
a
b
−
2
b
c
−
2
c
a
⟹
a
2
+
b
2
+
c
2
>
0
So the Roots are Real and Distinct
Suggest Corrections
0
Similar questions
Q.
The nature of the roots of
1
2
x
2
+
(
a
+
b
+
c
)
x
+
a
b
+
b
c
+
c
a
=
0
are
Q.
If
x
2
−
(
a
+
b
+
c
)
x
+
(
a
b
+
b
c
+
c
a
)
=
0
has imaginary roots, where
a
,
b
,
c
∈
R
+
,
then
√
a
,
√
b
,
√
c
Q.
Assertion :If the equation
x
2
+
b
x
+
c
a
=
0
and
x
2
+
c
x
+
a
b
=
0
have a common root, then their other root will satisfy the equation
x
2
+
a
x
+
b
c
=
0
Reason: If the equation
x
2
=
b
x
+
c
a
=
0
and
x
2
+
c
x
+
a
b
=
0
have a common root, then
a
+
b
+
c
=
0
Q.
If
x
2
+
a
x
+
b
c
=
0
and
x
2
+
b
x
+
c
a
=
0
(
a
≠
b
)
have a common root, then prove that their other roots satisfy the equation
x
2
+
c
x
+
a
b
=
0
.
Q.
If the quadratic equation
x
2
+
b
x
+
c
a
=
0
and
x
2
+
c
x
+
a
b
=
0
have a common root prove that the equation containing their other roots is
x
2
+
a
x
+
b
c
=
0
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 of Roots
MATHEMATICS
Watch in App
Explore more
Nature of Roots
Standard X 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