Statement-1: `If a ne 0` and the equation `ax^(2) + bx + c = 0` has two roots `alpha and beta` such that `alpha lt -1 and beta gt 1`, then a+|b|+c and a have the opposite sign.
Statement-2: `If ax^(2) + bx + c`, is same as that of 'a' for all real values of x except for those values of x lying between the roots.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Explanation

To solve the problem, we need to analyze the two statements provided and establish their validity based on the properties of quadratic equations.

### Step-by-Step Solution:

1. **Understanding the Quadratic Equation**:
We start with the quadratic equation given by:
\[ ax^2 + bx + c = 0 \]
where \( a \neq 0 \). The roots of this equation are denoted as \( \alpha \) and \( \beta \).

2. **Given Conditions**:
We know that:
- \( \alpha < -1 \)
- \( \beta > 1 \)

3. **Evaluating the Function at Specific Points**:
We will evaluate the quadratic function at \( x = 1 \) and \( x = -1 \):
- \( f(1) = a(1)^2 + b(1) + c = a + b + c \)
- \( f(-1) = a(-1)^2 + b(-1) + c = a - b + c \)

4. **Sign Analysis**:
Since \( \alpha < -1 \) and \( \beta > 1 \), the quadratic function \( f(x) \) will be:
- Positive for \( x < \alpha \)
- Negative between \( \alpha \) and \( \beta \)
- Positive for \( x > \beta \)

This means:
- \( f(1) < 0 \) (since \( 1 \) is between the roots)
- \( f(-1) < 0 \) (since \( -1 \) is also between the roots)

5. **Setting Up Inequalities**:
From the evaluations:
- \( a + b + c < 0 \) (from \( f(1) < 0 \))
- \( a - b + c < 0 \) (from \( f(-1) < 0 \))

6. **Combining Inequalities**:
We can rewrite the inequalities:
- From \( a + b + c < 0 \), we have:
\[ a + c < -b \]
- From \( a - b + c < 0 \), we have:
\[ a + c < b \]

7. **Analyzing Signs**:
We can combine these inequalities:
- Since \( a + c < -b \) and \( a + c < b \), it indicates that \( a + c \) must be less than both \( -b \) and \( b \).
- This implies that \( a + |b| + c < 0 \) if \( b \) is negative.

8. **Conclusion**:
Since \( a \) and \( a + |b| + c \) must have opposite signs, we conclude that:
- If \( a > 0 \), then \( a + |b| + c < 0 \) implies \( a + |b| + c \) is negative.
- If \( a < 0 \), then \( a + |b| + c > 0 \).

Thus, we can confirm that **Statement 1** is true, and **Statement 2** is also true based on the analysis of the behavior of the quadratic function.