Let `px^(2)+qx+r=0` be a quadratic equation `(p,q,r in R)` such that its roots are `alpha and beta`. If `p+q+rlt0,p-q+rlt0 and r gt0`, then the value of `[alpha]+[beta]` is (where[x] denotes the greatest integer x)________.

Explanation

To solve the problem step by step, we will analyze the given quadratic equation and the conditions provided.

### Step 1: Understand the Quadratic Equation
The given quadratic equation is:
\[ px^2 + qx + r = 0 \]
where \( p, q, r \) are real numbers and the roots are \( \alpha \) and \( \beta \).

### Step 2: Use Vieta's Formulas
According to Vieta's formulas, the sum of the roots \( \alpha + \beta \) can be expressed as:
\[ \alpha + \beta = -\frac{q}{p} \]

### Step 3: Analyze the Conditions
We have the following conditions:
1. \( p + q + r < 0 \)
2. \( p - q + r < 0 \)
3. \( r > 0 \)

### Step 4: Evaluate the Conditions
1. From \( p + q + r < 0 \), we can infer that \( p + q < -r \).
2. From \( p - q + r < 0 \), we can infer that \( p - q < -r \).
3. Since \( r > 0 \), this means \( -r < 0 \).

### Step 5: Substitute Values
Now, let's evaluate the function \( f(x) = px^2 + qx + r \) at specific points:
- When \( x = 0 \):
\[ f(0) = r > 0 \]
- When \( x = 1 \):
\[ f(1) = p + q + r < 0 \]
- When \( x = -1 \):
\[ f(-1) = p - q + r < 0 \]

### Step 6: Identify the Roots
From the evaluations:
- Since \( f(0) > 0 \) and \( f(1) < 0 \), by the Intermediate Value Theorem, there is a root \( \alpha \) in the interval \( (0, 1) \).
- Since \( f(-1) < 0 \) and \( f(0) > 0 \), there is a root \( \beta \) in the interval \( (-1, 0) \).

### Step 7: Determine the Greatest Integer Values
- Since \( \alpha \) lies between \( 0 \) and \( 1 \), the greatest integer value \( [\alpha] = 0 \).
- Since \( \beta \) lies between \( -1 \) and \( 0 \), the greatest integer value \( [\beta] = -1 \).

### Step 8: Calculate the Final Result
Now, we can find:
\[ [\alpha] + [\beta] = 0 + (-1) = -1 \]

### Conclusion
Thus, the value of \( [\alpha] + [\beta] \) is:
\[ \boxed{-1} \]