find the number of zeroes of given polynomials f(x)=(x-2)square +4
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We have,
f(x)=x
2
−2
=x
2
−(
2
)
2
=(x−
2
)(x+
2
)
The zeroes off(x) are given by f(x)=0
(x−
2
)(x+
2
)=0
(x−
2
)=0 or,(x+
2
)=0
x=
2
or x=−
2
Thus ,the zeroes of f(x) are α=
2
and β=−
2
Now,
Sum of the zeroes=α+β=
2
+(−
2
)
=0
and, −(
coefficient of x
2
coefficient of x
)=−(
1
0
)=0
Therefore sum of the zeroes=−(
coefficient of x
2
coefficient of x
)
Product of the zeroes=α×β=
2
×−
2
=−2
and,
coefficient of x
2
constant term
=
1
−2
=−2
Therefore, product of zeros =
coefficient of x
2
constant term
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