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Byju's Answer
Standard XII
Mathematics
Common Roots
Maximum numbe...
Question
Maximum number of real roots does the equation ax¹⁰-bx⁸+cx²+e=0 ,a,b,c,e>0 can have.
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Similar questions
Q.
Assertion :If
a
+
b
+
c
>
0
,
a
<
0
<
b
<
c
, then roots of the equation
a
(
x
−
b
)
(
x
−
c
)
+
b
(
x
−
c
)
(
x
−
a
)
+
c
(
x
−
a
)
(
x
−
b
)
=
0
are real. Reason: Roots of the equation
A
x
2
+
B
x
+
K
=
0
are real if
B
2
−
4
A
K
>
0
.
Q.
Find the number of real roots of the equation
∣
∣ ∣
∣
0
x
−
a
x
−
b
x
+
a
0
x
−
c
x
+
b
x
+
c
0
∣
∣ ∣
∣
=
0
,
a
≠
b
≠
c
,
b
(
a
+
c
)
>
a
c
Q.
Equation
x
4
+
a
x
3
+
b
x
2
+
c
x
+
1
=
0
has real roots (
a
,
b
,
c
a
,
b
,
c
are non-negative). Maximum real value of
c
is
Q.
If
a
,
b
,
c
,
d
,
e
are real numbers,show that the roots of
x
5
+
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
=
0
cannot all be real, if
2
a
2
<
5
b
.
Q.
One root of
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
=
0
, where
a
,
b
,
c
,
d
,
e
are rational numbers, is
√
2
+
√
3
, then the other real roots are:
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