Root of x³ + 4 x² + x - 6
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Explanation:
Provided the expression has rational roots, we can use the rational root theorem.
For the expression
x
3
−
4
x
2
+
x
+
6
according to the rational root theorem, possible rational roots are:
XXX
{
±
1
,
±
2
,
±
3
,
±
6
}
With the use of a spreadsheet these values can be easily checked (it can also be done with a calculator or even manually with a bit more effort).
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From this, we see that
x
=
2
,
x
=
3
, and
x
=
−
1
all are zeros for the given expression.
This implies that
(
x
−
2
)
,
(
x
−
3
)
, and
(
x
+
1
)
are factors of the given expression.
Since
x
3
−
4
x
2
+
x
+
6
is of degree
3
, it has a maximum of
3
factors and we have found them a
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