Question

Find the roots of f(x) = (e
x − e
π
)(e
x − π) where e denotes Euler’s number.

Answer 1

The function given to us is: $f(x) = (ex-e\pi)(ex-\pi)$

We know that the roots of this equation will be the those values of $x$ that will make the value of the function $f(x)=0$. Thus, the roots can be found as:

$(ex-e\pi)(ex-\pi)=0$

Therefore, either $(ex-e\pi)=0$ or $(ex-\pi)=0$

Thus, from the first one we will get: $x=\pi$ as one root and from the other equation we will get:

$x=\frac{\pi}{e}$

for the second root.

Answer 2

The function given to us is:

f(x) = (ex-eπ) (ex-π)

We know that the roots of this equation will be the those values of  that will make the value of the function f(x). Thus, the roots can be found as:

(ex-eπ) (ex-π) = 0

Therefore either, (ex-eπ) = 0 or (ex-π) = 0

Thus, from the first one we will get:  as one root and from the other equation we will get:

x = π/e

for the second root.