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Byju's Answer
Standard X
Mathematics
Formation of a Quadratic Equation From It's Roots
A quadratic p...
Question
A quadratic polynomial whose zeros are
3
5
and
-
1
2
,is
(a) 10x
2
+ x + 3
(b) 10x
2
+ x − 3
(c) 10x
2
− x + 3
(d)
x
2
-
1
10
x
-
3
10
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Solution
(
d
)
x
2
−
1
10
x
−
3
10
Here, the zeroes are
3
5
and
−
1
2
.
Let
α
=
3
5
a
n
d
β
=
−
1
2
So, sum of the zeroes, α+β=
3
5
+
−
1
2
=
1
10
Also, product of the zeroes, αβ=
3
5
×
−
1
2
=
−
3
10
The
polynomial
will
be
x
2
-
(
α
+
β
)
x
+
α
β
.
∴
The
r
equired polynomial is
x
2
−
1
10
x
−
3
10
.
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