Find the value of the polynomial `5x-4x^(2)+3` at (a) x=0 (b) x=1

Answer

To find the value of the polynomial \( P(x) = 5x - 4x^2 + 3 \) at the given values of \( x \), we will evaluate the polynomial for both parts of the question.

### Part (a): Find \( P(0) \)

1. **Substitute \( x = 0 \) into the polynomial:**
\[ P(0) = 5(0) - 4(0)^2 + 3 \]

2. **Calculate each term:**
- The first term: \( 5(0) = 0 \)
- The second term: \( -4(0)^2 = 0 \)
- The third term: \( +3 = 3 \)

3. **Combine the results:**
\[ P(0) = 0 - 0 + 3 = 3 \]

Thus, the value of the polynomial at \( x = 0 \) is **3**.

### Part (b): Find \( P(1) \)

1. **Substitute \( x = 1 \) into the polynomial:**
\[ P(1) = 5(1) - 4(1)^2 + 3 \]

2. **Calculate each term:**
- The first term: \( 5(1) = 5 \)
- The second term: \( -4(1)^2 = -4 \)
- The third term: \( +3 = 3 \)

3. **Combine the results:**
\[ P(1) = 5 - 4 + 3 = 1 + 3 = 4 \]

Thus, the value of the polynomial at \( x = 1 \) is **4**.

### Summary of Results:
- \( P(0) = 3 \)
- \( P(1) = 4 \)