60 points
2 answers:
You might be interested in
Answer:
x = 16
Step-by-step explanation:
The product of the lengths theorem is a property that can be sued to describe the relationships of the sides between the tangents and secants in a circle. One of these products states the following;
The distance between the point of tangency and its intersection point with the exterior secant squared is equal to the product of the exterior secant times the interior secant.
This essentially means the following equation can be formed;
Substitute,
Simplify,
Inverse operations,
Solution:
There is no (zero) complex zeros for the given polynomial.
Explanation:
We apply Descartes' rule of sign to identify the number of complex roots.
The given polynomial is
Let us see the number of sign changes in f(x)
+,-,+
There are 2 sign changes in f(x). One from plus to minus and second from plus to minus. Hence, there 2 or 0 positive roots.
Now, let us see the number of sign changes in f(-x)
-,-,+
There are only one sign change. Hence, there will be 1 negative roots.
The degree of the polynomial is 3. Hence, there will be exactly 3 zeros.
Therefore, the possible numbers of zeros are
2 positive, 1 negative and 0 complex
0 positive, 1 negative and 2 complex.
Hence, possible number of complex zeros are 0 and 2.
Now, we graph the function in xy plane and see that the graph cuts the x axis at three points. It means all the zeros are real , which is the case of first possibility (2 positive, 1 negative and 0 complex).
Hence, the number of complex zeros for the given polynomial is zero.
