RBSE class fifth chapter number chapter number 14 in maths
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Class 10
>>Maths
>>Polynomials
>>Relationship between Zeroes and Coefficients of a Polynomial
>>Find the zeroes of the following polynom
Question
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Find the zeroes of the following polynomials by factorisation method and verify the relation between the zeroes and the coefficients of the polynomials:
4x
2
+5
2
x−3
Medium
Solution
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4x
2
+5
2
x−3
=4x
2
+6
2
x−
2
x−3
=2
2
x(
2
x+3)−(
2
x+3)
=(
2
x+3)(2
2
x−1)
So, the zeros of the polynomial are
(
2
x+3)=0 and (2
2
x−1)=0
x=
2
−3
and x=
2
2
1
x=
2
−3
2
and x=
4
2
Now, the polynomial is 4x
2
+5
2
x−3
Comparing it with ax
2
+bx+c=0, we get a=4, b=5
2
and c=−3
Sum of the zeros =
2
−3
2
+
4
2
=
4
−6
2
+
2
=
4
−5
2
=
a
−b
Product of the zeros =(
2
−3
2
)(
4
2
)
=(
2
−3
)(
4
2
)
=
4
−3
=
a
c
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