If `x^3+3x^2-9x+c` is of the form `(x-alpha)^2(x-beta)` then `c` is equal to

Options

A. 27
B. `-27`
C. 5
D. -5

Explanation

To solve the problem, we need to find the value of \( c \) such that the polynomial \( x^3 + 3x^2 - 9x + c \) can be expressed in the form \( (x - \alpha)^2 (x - \beta) \).

### Step-by-Step Solution:

1. **Understanding the Form**:
We know that if \( x^3 + 3x^2 - 9x + c = (x - \alpha)^2 (x - \beta) \), then \( \alpha \) is a double root and \( \beta \) is a single root.

2. **Finding the Derivative**:
...