I am going to use the root-location theorem.Originally Posted bySusie38

If is countinous on and have opposite signs then there exists a number such as, .

You have, thus,

Find the critical points,

Thus, but since we have, thus there are no critical points (because it yields imaginary numbers). Because the function is always increasing. Meaning that it intersects the x-axis only once. Thus, there is only one real root.

Actually that is not necessarily true. It would have been correct to state that since,Originally Posted byThePerfectHacker

We can make the function as large and as small as we like. Meaning that we can choose values such as it is negative and positive. Then apply the root location theorem.