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Byju's Answer
Standard XI
Mathematics
Transformation of Roots: Linear Combination of Roots
If the roots ...
Question
If the roots of
x
2
+
m
x
+
n
=
0
are twice the roots of
x
2
+
p
x
+
m
=
0
,
p
≠
0
, then the value of
n
p
is
A
8
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B
8.00
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C
8.0
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Solution
Let the roots of
x
2
+
p
x
+
m
=
0
be
α
,
β
α
+
β
=
−
p
and
α
β
=
m
⋯
(
1
)
Roots of
x
2
+
m
x
+
n
=
0
are
2
α
,
2
β
⇒
2
α
+
2
β
=
−
m
and
2
α
⋅
2
β
=
n
⇒
2
(
α
+
β
)
=
−
m
and
4
α
β
=
n
⇒
2
p
=
m
and
4
m
=
n
[
Using
(
1
)
]
⇒
8
p
=
n
⇒
n
p
=
8
Suggest Corrections
0
Similar questions
Q.
If the roots of
x
2
+
m
x
+
n
=
0
are twice the roots of
x
2
+
p
x
+
m
=
0
,
p
≠
0
, then the value of
n
p
is
Q.
If the roots of
x
2
+
m
x
+
n
=
0
are twice the roots of
x
2
+
p
x
+
m
=
0
,
p
≠
0
, then the value of
n
p
is
Q.
Let
m
,
n
be positive integers and the quadratic equation
4
x
2
+
m
x
+
n
=
0
has two distinct real roots
p
and
q
(
p
≤
q
)
. Also, the quadratic equations
x
2
−
p
x
+
2
q
=
0
and
x
2
−
q
x
+
2
p
=
0
have a common root say
α
.
If
p
and
q
are rational, then uncommon root of the equation
x
2
−
p
x
+
2
q
=
0
and
x
2
−
q
x
+
2
p
=
0
is equal to
Q.
If
x
2
+
p
x
+
25
=
0
, has equal roots, then the value of
p
(
p
>
0
)
is
Q.
If roots of equation of
x
2
+
x
+
1
=
0
are
a
,
b
and roots of
x
2
+
p
x
+
q
=
0
are
a
b
,
b
a
then value of
p
+
q
is
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