How many zero(es) does the polynomial `293x^(2)-293x` have ?

Options

A. 0
B. 1
C. 2
D. 3

Answer

To determine how many zeros the polynomial \( 293x^2 - 293x \) has, we can follow these steps:

### Step 1: Set the polynomial equal to zero
We start by setting the polynomial equal to zero to find the values of \( x \) that make the polynomial zero:
\[ 293x^2 - 293x = 0 \]

### Step 2: Factor the polynomial
Next, we can factor out the common term from the polynomial:
\[ 293x(x - 1) = 0 \]

### Step 3: Apply the zero product property
According to the zero product property, if the product of two factors equals zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero:
1. \( 293x = 0 \)
2. \( x - 1 = 0 \)

### Step 4: Solve for \( x \)
Now we solve each equation:
1. From \( 293x = 0 \):
\[ x = 0 \]
2. From \( x - 1 = 0 \):
\[ x = 1 \]

### Step 5: Count the number of zeros
We found two values of \( x \) that make the polynomial equal to zero: \( x = 0 \) and \( x = 1 \). Therefore, the polynomial has **2 zeros**.

### Final Answer
The polynomial \( 293x^2 - 293x \) has **2 zeros**.

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