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Standard X
Mathematics
Relationship between Zeroes and Coefficients of a Polynomial
If one zero o...
Question
If one zero of the polynomial
(
a
2
+
9
)
x
2
+
13
x
+
6
a
is reciprocal of the other, find the value of a
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Solution
⇒
The given quadratic polynomial is
(
a
2
+
9
)
x
2
+
13
x
+
6
a
.
⇒
Let one zero of the quadratic polynomial be
α
.
∴
The other zero of the quadratic polynomial is
1
α
.
⇒
α
×
1
α
=
6
a
a
2
+
9
⇒
1
=
6
a
a
2
+
9
⇒
a
2
+
9
=
6
a
⇒
a
2
−
6
a
+
9
=
0
⇒
(
a
−
3
)
2
=
0
⇒
a
−
3
=
0
⇒
a
=
3
∴
The value of
a
is
3
.
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