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Byju's Answer
Standard X
Mathematics
Geometric Progression
The cubic equ...
Question
The cubic equation whose roots are each 2 more than the roots of the equation
x
3
+
4
x
2
−
3
x
+
12
=
0
is
A
x
3
+
2
x
2
−
31
x
−
2
=
0
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B
x
3
+
6
x
2
−
x
+
14
=
0
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C
x
3
−
2
x
2
−
7
x
+
26
=
0
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D
x
3
+
2
x
2
−
5
x
+
10
=
0
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Solution
The correct option is
C
x
3
−
2
x
2
−
7
x
+
26
=
0
Let
x
3
+
4
x
2
−
3
x
+
12
=
0
We know that sum of roots
α
+
β
+
γ
=
−
4
1
=
−
4
When each root is increased by 2,
So new roots will be
α
+
2
,
β
+
2
,
γ
+
2
Hence, sum of roots
=
α
+
β
+
γ
+
6
=
−
4
+
6
=
2
So, the coefficient of
x
2
will be
−
2
1
Hence, Correct option is
C
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0
Similar questions
Q.
Number of common roots of the equation
x
3
−
2
x
2
−
x
+
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=
0
and
x
3
+
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+
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x
+
6
=
0
is
Q.
The roots of the equation
x
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+ 2
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Q.
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p
,
q
,
r
be roots of cubic equation
x
3
+
2
x
2
+
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+
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=
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Q.
Find the equation whose root are square of the root are
x
3
−
2
x
2
−
x
+
5
=
0
Q.
Assertion (A): The equation whose roots are squares of the roots of
x
3
−
2
x
2
−
2
x
+
3
=
0
is
x
3
−
8
x
2
+
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x
−
9
=
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.
Reason (R): The equation whose roots are the square of the roots of
f
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is
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(
√
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=
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