if both x-2 and `x-(1)/(2)` are factors of `px^(2)+5x+r.` then show that p=r.

Explanation

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

### Step-by-Step Solution:

1. **Identify the Polynomial**:
We have the polynomial \(f(x) = px^2 + 5x + r\).

2. **Use the Factor Theorem**:
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