"If  a continuous function `f`defined  on the real line `R ,`assumes  positive and negative
Channel: Doubtnut
Date: 2020-04-12

"If
  a continuous function `f`
defined
  on the real line `R ,`
assumes
  positive and negative values in `R`
then
  the equation `f(x)=0`
has
  a root in `R`
.
  For example, if it is known that a continuous function `f`
on
  `R`
is
  positive at some point and its minimum value is negative then the equation `f(x)=0`
has
  a root in `Rdot`

Consider
  `f(x)=k e^x-x`
for
  all real `x`
where `k`
is
  a real constant
The
  line `y=x`
meets
  `y=k e^x`
for
  `klt=0`
at
no
  point (b) one point
two
  points (d) more than two points"