The zero (s) of the polynomial `z^(2)-2z` is (are):-

Options

A. 0
B. 2z
C. 2
D. 0,2

Answer

To find the zeros of the polynomial \( z^2 - 2z \), we will follow these steps:

### Step 1: Set the polynomial equal to zero
We start by setting the polynomial equal to zero to find its zeros:
\[ z^2 - 2z = 0 \]

### Step 2: Factor the polynomial
Next, we can factor the left-hand side of the equation. We can take \( z \) as a common factor:
\[ z(z - 2) = 0 \]

### Step 3: Apply the zero product property
According to the zero product property, if the product of two factors is zero, at least one of the factors must be zero. Therefore, we can set each factor equal to zero:
1. \( z = 0 \)
2. \( z - 2 = 0 \)

### Step 4: Solve for \( z \)
From the first factor, we have:
\[ z = 0 \]
From the second factor, we solve for \( z \):
\[ z - 2 = 0 \implies z = 2 \]

### Conclusion
The zeros of the polynomial \( z^2 - 2z \) are:
\[ z = 0 \quad \text{and} \quad z = 2 \]

### Summary
Thus, the required zeros of the polynomial are \( 0 \) and \( 2 \).

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