Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
u
(
x
)
=
x
2
+
k
x
+
2
u(x)=x^{2}+kx+2
u
(
x
)
=
x
2
+
k
x
+
2
and
v
(
x
)
=
x
+
k
v(x)=x+k
v
(
x
)
=
x
+
k
, where
k
∈
R
k\in\mathbb{R}
k
∈
R
. (i) For which real value(s) of
x
x
x
is the quotient
u
(
x
)
v
(
x
)
\dfrac{u(x)}{v(x)}
v
(
x
)
u
(
x
)
not defined? (ii) If the coefficient of
x
x
x
in the product
u
(
x
)
v
(
x
)
u(x)\,v(x)
u
(
x
)
v
(
x
)
equals
10
10
10
, find the possible value(s) of
k
k
k
.
Browse the problem library