The sum of the coefficients in `(1+x-3x^2)^2143` is

Options

A. (a) `2^2143`
B. (b)0
C. (c)1
D. (d)-1

Answer

To find the sum of the coefficients in the expression \((1 + x - 3x^2)^{2143}\), we can follow these steps:

### Step 1: Understand the Concept
The sum of the coefficients of a polynomial can be found by substituting \(x = 1\) into the polynomial. This is because each term in the polynomial contributes its coefficient when \(x\) is set to 1.

### Step 2: Substitute \(x = 1\)
We substitute \(x = 1\) into the expression:
\[ 1 + x - 3x^2 \rightarrow 1 + 1 - 3(1^2) \]

### Step 3: Simplify the Expression
Now simplify the expression:
\[ 1 + 1 - 3(1) = 1 + 1 - 3 = 2 - 3 = -1 \]

### Step 4: Raise to the Power
Now we raise this result to the power of \(2143\):
\[ (-1)^{2143} \]

### Step 5: Determine the Result
Since \(2143\) is an odd number, \((-1)^{2143} = -1\).

### Final Answer
Thus, the sum of the coefficients in the expression \((1 + x - 3x^2)^{2143}\) is \(-1\).