If `A(1,p^(2)),B(0,1)` and `C(p,0)` are the coordinates of three points then area of the triangle `ABC` is `1/(lamda)|p^(3)-p+1|`. The value of `lamda` is

Explanation

To find the value of \(\lambda\) in the given problem, we will calculate the area of triangle \(ABC\) using the coordinates of points \(A(1, p^2)\), \(B(0, 1)\), and \(C(p, 0)\).

### Step-by-Step Solution:

1. **Identify the Coordinates**:
The coordinates of the points are:
- \(A(1, p^2)\)
- \(B(0, 1)\)
- \(C(p, 0)\)

2. **Use the Area Formula**:
The area \(A\) of triangle formed by three points \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) can be calculated using the formula:
\[ A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]

3. **Substitute the Coordinates**:
Substituting the coordinates of points \(A\), \(B\), and \(C\) into the formula:
\[ A = \frac{1}{2} \left| 1(1 - 0) + 0(0 - p^2) + p(p^2 - 1) \right| \]
Simplifying this expression:
\[ A = \frac{1}{2} \left| 1 + p(p^2 - 1) \right| \]
\[ A = \frac{1}{2} \left| 1 + p^3 - p \right| \]
\[ A = \frac{1}{2} \left| p^3 - p + 1 \right| \]

4. **Equate to Given Area**:
We are given that the area is equal to \(\frac{1}{\lambda} |p^3 - p + 1|\). Thus, we have:
\[ \frac{1}{2} |p^3 - p + 1| = \frac{1}{\lambda} |p^3 - p + 1| \]

5. **Cancel the Absolute Values**:
Assuming \( |p^3 - p + 1| \neq 0 \), we can cancel it from both sides:
\[ \frac{1}{2} = \frac{1}{\lambda} \]

6. **Solve for \(\lambda\)**:
Rearranging gives:
\[ \lambda = 2 \]

### Final Answer:
The value of \(\lambda\) is \(2\).