find zeroes of the polynomial x³+4x²-25x-100 and verify the relation between zeroes and coefficients
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find zeroes of the polynomial x³+4x²-25x-100 and verify the relation between zeroes and coefficients
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Answer:
do this step
Step-by-step explanation:
x
3
+
4
x
2
−
25
x
−
100
=
x
2
(
x
+
4
)
−
25
(
x
+
4
)
=
(
x
2
−
25
)
(
x
+
4
)
Now you can use the identity
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
to factorize further:
...
=
(
x
+
5
)
(
x
−
5
)
(
x
+
4
)
Now,
f
(
x
)
=
0
⇔
x
3
+
4
x
2
−
25
x
−
100
=
0
⇔
(
x
+
5
)
(
x
−
5
)
(
x
+
4
)
=
0
A product is equal to zero if one or more factors is/are equal to zero:
⇔
x
+
5
=
0
or
x
−
5
=
0
or
x
+
4
=
0
⇔
x
=
−
5
or
x
=
5
or
x
=
−
4