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Byju's Answer
Standard X
Mathematics
Relationship between Zeroes and Coefficients of a Polynomial
Find the zero...
Question
Find the zeroes of the polynomial x square + 1/6x - 2 , and verify the relation between the coefficients and the zeroes of the polynomial .
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Solution
Let
p
x
=
x
2
+
x
6
-
2
Now
,
zeroes
of
p
x
are
given
by
solving
the
equation
p
x
=
0
⇒
x
2
+
x
6
-
2
=
0
⇒
6
x
2
+
x
-
12
=
0
⇒
6
x
2
+
9
x
-
8
x
-
12
=
0
⇒
3
x
2
x
+
3
-
4
2
x
+
3
=
0
⇒
3
x
-
4
2
x
+
3
=
0
⇒
3
x
-
4
=
0
or
2
x
+
3
=
0
⇒
x
=
4
3
or
x
=
-
3
2
Now
,
sum
of
zeroes
=
4
3
+
-
3
2
=
4
3
-
3
2
=
8
-
9
6
=
-
1
6
=
-
coefficient
of
x
coefficient
of
x
2
product
of
zeroes
=
4
3
×
-
3
2
=
-
2
=
constant
term
coefficient
of
x
2
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