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Byju's Answer
Standard XII
Mathematics
Definition of Functions
The product o...
Question
The product of two zeroes of the polynomial
p
(
x
)
=
x
3
−
3
x
2
−
6
x
+
8
is
(
−
2
)
.
Find all the zeroes of the polynomial.
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Solution
Given,
p
(
x
)
=
x
3
−
3
x
2
−
6
x
+
8
.
Let
α
,
β
&
γ
be zeroes of
p
(
x
)
.
Then,
α
β
γ
=
−
8
,
α
+
β
+
γ
=
3
,
α
β
+
β
γ
+
γ
α
=
−
6
.
According to question,
α
β
=
−
2
.
∴
γ
=
4
.
α
+
β
=
3
−
4
=
−
1
.
⇒
α
β
=
−
2
&
α
+
β
=
−
1
⇒
α
(
−
1
−
α
)
=
−
2
⇒
−
α
−
α
2
=
−
2
⇒
α
2
+
α
−
2
=
0
⇒
α
=
1
or
α
=
−
2
.
∴
Zeroes are
1
,
−
2
,
4
.
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Similar questions
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If two zeroes of the polynomial p(x) = 2x
4
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Q.
If two zero of the polynomial
p
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)
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x
4
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x
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−
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√
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Q.
Find all the zeros of the polynomial x
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.