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Mathematics
Mathematics
Problem
Let
p
(
x
)
=
x
3
+
(
k
−
5
)
x
2
+
(
k
−
2
)
x
+
4
,
p(x)=x^{3}+(k-5)x^{2}+(k-2)x+4,
p
(
x
)
=
x
3
+
(
k
−
5
)
x
2
+
(
k
−
2
)
x
+
4
,
where
k
k
k
is a real number. (i) If
x
=
1
x=1
x
=
1
is a zero of
p
(
x
)
p(x)
p
(
x
)
, determine the value of
k
k
k
. (ii) For the value of
k
k
k
obtained in part (i), factorise
p
(
x
)
p(x)
p
(
x
)
completely and write down all its real zeros.
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