If both `x-2` and `x-1/2` are factors of `p x^2+5x+r ,` show that `p=rdot`

Explanation

To solve the problem, we need to show that if both \( x - 2 \) and \( x - \frac{1}{2} \) are factors of the polynomial \( p x^2 + 5x + r \), then \( p = r \).

### Step-by-Step Solution:

1. **Identify the Factors**:
Since \( x - 2 \) and \( x - \frac{1}{2} \) are factors of the polynomial, we can express the polynomial as:
\[
p x^2 + 5x + r = (x - 2)\left(x - \frac{1}{2}\right)
...