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Chapter 2: Problem 13

Determine the number of zeros of the polynomial function. $$f(x)=(x+5)^{2}$$

Short Answer

Expert verified
The polynomial function \(f(x)=(x+5)^{2}\) has one zero, which is \(x = -5\).

Step by step solution

01

Setup the equation

Set the function equal to zero, i.e., \((x+5)^{2}=0\).
02

Solve the equation

Solving the above equation, we find that it is a simple square root equation - one where if we take the square root of both sides, we can isolate \(x\). However, remember to account for both positive and negative square root possibilities. In this case, the equation simplifies to \(x+5 = 0\) or \(x+5 = 0\).
03

Solution

After solving both equations, we find that both have the same solution, i.e. \(x = -5\). Hence, even though this root shows up twice, it is only counted as one root. This is because it is the same root that appears twice, rather than two distinct roots.

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