Let `f(x)` be a quadratic polynomial with `f(2)=-2`. Then the coefficient of `x` in `f(x)` is-

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To solve the problem, we need to determine the coefficient of \( x \) in the quadratic polynomial \( f(x) \). We know that \( f(2) = -2 \).

Let's denote the quadratic polynomial as:

\[ f(x) = ax^2 + bx + c \]

### Step 1: Set up the equations using the given information
Given that \( f(2) = -2 \), we can substitute \( x = 2 \) into the polynomial:

\[ f(2) = a(2^2) + b(2) + c = 4a + 2b + c = -2 \]

This gives us our first equation:

\[ 4a + 2b + c = -2 \quad \text{(1)} \]

### Step 2: Use the second condition
We are also given that \( f(-2) = -2 \). Substituting \( x = -2 \) into the polynomial gives:

\[ f(-2) = a(-2^2) + b(-2) + c = 4a - 2b + c = -2 \]

This gives us our second equation:

\[ 4a - 2b + c = -2 \quad \text{(2)} \]

### Step 3: Subtract the two equations
Now we will subtract equation (2) from equation (1):

\[ (4a + 2b + c) - (4a - 2b + c) = -2 - (-2) \]

This simplifies to:

\[ 4b = 0 \]

### Step 4: Solve for \( b \)
From the equation \( 4b = 0 \), we can solve for \( b \):

\[ b = 0 \]

### Conclusion
The coefficient of \( x \) in the polynomial \( f(x) \) is \( b \), which we found to be \( 0 \).

Thus, the answer is:

\[ \text{The coefficient of } x \text{ in } f(x) \text{ is } 0. \]