Find the Zeroes of
and verify the relationship between the zeroes and the coefficients.
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10th
Maths
Polynomials
Relationship between Zeroes and Coefficients of a Polynomial
Find the zeros of the polyn...
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Asked on December 20, 2019 by
Mannat Sapra
Find the zeros of the polynomial 3
2
x
2
+13x+6
2
and verify the relationship between the zeros.
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ANSWER
Let us first factorize the given equation 3
2
x
2
+13x+6
2
as shown below:
⇒3
2
x
2
+13x+6
2
=3
2
x
2
+9x+4x+6
2
=3x(
2
x+3)+2
2
(
2
x+3)
=(3x+2
2
)(
2
x+3)
Therefore, the zeroes of the given polynomial are:
(3x+2
2
)=0
⇒x=−
3
2
2
=α
(
2
x+3)=0
⇒x=−
2
3
=β
Now, the sum and product of the roots is as follows:
α+β=−
3
2
2
−
2
3
=−(
3
2
2
+
2
3
)=
3
2
−4−9
=−
3
2
13
=−
a
b
αβ=(−
3
2
2
)(−
2
3
)=
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Given.
The quadratic polynomial 2x² - 8x + 6 and verify the relationship between the zeroes and it's coefficient.
Tofind:
The zeroes.
Explanation:
We have, quadratic polynomial = 2x² - 8x
⇝2x
2
−8x+6=0
⇝2x
2
−6x−2x+6=0
⇝2x(x−3)−2(x−3)=0
⇝(x−3)(2x−2)=0
⇝(x−3)=0Or(2x−2)=0
⇝x−3=0Or2x−2=0
⇝x=3Or2x=2
⇝x=3Orx=
2
2
⇝x=3Orx=1
Thus,
\bf{\large{\underline{\sf{\red{We\:have\:zeroes\:are\:\alpha =3\:\:\&\:\:\beta =1.}}}}}
Wehavezeroesareα=3&β=1.
∴ Relation between the zeroes and it's coefficient :
From quadratic polynomial :
a = 2
b = -8
c = 6