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Mathematics
Problem
Consider the quadratic function
q
(
x
)
=
2
x
2
+
k
x
+
8
q(x)=2x^{2}+kx+8
q
(
x
)
=
2
x
2
+
k
x
+
8
. For which set of real numbers
k
k
k
is
q
(
x
)
>
0
q(x)>0
q
(
x
)
>
0
for all real
x
x
x
? a)
k
∈
(
−
∞
,
−
8
)
∪
(
8
,
∞
)
k\in(-\infty,-8)\cup(8,\infty)
k
∈
(
−
∞
,
−
8
)
∪
(
8
,
∞
)
b)
k
∈
(
−
4
2
,
4
2
)
k\in(-4\sqrt{2},4\sqrt{2})
k
∈
(
−
4
2
,
4
2
)
c)
k
∈
(
−
8
,
8
)
k\in(-8,8)
k
∈
(
−
8
,
8
)
d)
k
=
−
8
or
k
=
8
k=-8 \text{ or } k=8
k
=
−
8
or
k
=
8
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