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Byju's Answer
Standard XII
Mathematics
Nature of Roots of a Cubic Polynomial Using Derivatives
If a, b and c...
Question
If a, b and c are odd integers then prove that roots of ax²+bx+c=0 cannot be rational.
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Similar questions
Q.
If
a
+
b
+
c
=
0
, prove that the roots of
a
x
2
+
b
x
+
c
=
0
are rational. Hence, show that the roots of
(
p
+
q
)
x
2
−
2
p
x
+
(
p
−
q
)
=
0
are rational.
Q.
If the coefficients of the quadratic equation
a
x
2
+
b
x
+
c
=
0
are odd integers, then the roots of the equation cannot be
Q.
Assertion :If
a
,
b
,
c
∈
Q
and
2
1
3
is a root of
a
x
2
+
b
x
+
c
=
0
,
t
h
e
n
a
=
b
=
c
=
0
. Reason: A polynomial equation with rational coefficients cannot have irrational roots
Q.
Let
a
and
c
be odd prime numbers and
b
be an integer. If the quadratic equation
a
x
2
+
b
x
+
c
=
0
has rational roots, then which of the following statement(s) is/are correct?
Q.
If both the roots of the quadratic equation
a
x
2
+
b
x
+
c
=
0
are negative, then
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