angie07253
26.10.2020 •
Mathematics
Find all rational zeros of P(x) = x3 - 7x + 6
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Ответ:
Zeros are
x
=
−
1
,
x
=
−
2
and
x
=
3
Explanation:
f
(
x
)
=
x
3
−
7
x
−
6
;
By inspection
f
(
−
1
)
=
0
,so
(
x
+
1
)
will be a factor.
x
3
−
7
x
−
6
=
x
3
+
x
2
−
x
2
−
x
−
6
x
−
6
=
x
2
(
x
+
1
)
−
x
(
x
+
1
)
−
6
(
x
+
1
)
=
(
x
+
1
)
(
x
2
−
x
−
6
)
=
(
x
+
1
)
(
x
2
−
3
x
+
2
x
−
6
)
=
(
x
+
1
)
{
x
(
x
−
3
)
+
2
(
x
−
3
)
}
∴
f
(
x
)
=
(
x
+
1
)
(
x
−
3
)
(
x
+
2
)
∴
f
(
x
)
will be zero
for
x
=
−
1
,
x
=
−
2
and
x
=
3
Hence zeros are
x
=
−
1
,
x
=
−
2
and
x
=
3
[Ans]
Step-by-step explanation:
Ответ: