Video Transcript
What are the zeros of 𝑓 of 𝑥
equal to 𝑥 plus 𝜋 squared minus 𝑒?
First, we copy down our
problem. And then in place of 𝑓 of 𝑥, we
want to put a zero. We’re looking for the place where
𝑓 of 𝑥 is equal to zero. And then, we can solve this using
algebra. We’re trying to isolate 𝑥, get 𝑥
by itself.
The first thing I can do is get rid
of the 𝑒 by adding 𝑒 to the right side of the equation. If we add 𝑒 to the right, we have
to add 𝑒 to the left. Negative 𝑒 plus 𝑒 equals
zero. Zero plus 𝑒 equals 𝑒. Our equation now says 𝑒 is equal
to 𝑥 plus 𝜋 squared. To get rid of the square, we take
the square root of 𝑥 plus 𝜋 squared.
But if we take the square root on
the right, we need to take the square root on the left. On the right side of the equation,
the only thing that remains is 𝑥 plus 𝜋. The left side is a little bit
different. On the left side, we need to say
that we have two options: we have the positive square root of 𝑒 and the negative
square root of 𝑒. We have two cases.
There is no reason for our
parentheses anymore. So we can drop those and then we
subtract 𝜋 from both sides of the equation. Positive 𝜋 minus 𝜋 equals
zero. 𝑥 is by itself on the right
side. On the left side, there is nothing
really that we can simplify. We can just say negative 𝜋 plus or
minus the square root of 𝑒.
And this is how we break that down
into two different options: 𝑥 could be equal to negative 𝜋 plus 𝑒 or negative 𝜋
minus the square root of 𝑒.
This function has two zeros:
negative 𝜋 plus the square root of 𝑒 and negative 𝜋 minus the square root of
𝑒.
