Assertion (A): The zeroes of the polynomial `p(x)=x^(3)+3x^(2)-4x-12` are -2,2 and 3.
Reason (R):Sum of zeroes `=(-b)/a`
and product of zeroes `=c/a`

Options

A. Both A and R are true and R is the correct explanation for a
B. Both A and R are true and R is not correct explanation for A.
C. A is true but R is false.
D. A is false but R is true

Answer

To solve the question regarding the assertion and reason type statement, let's break it down step by step.

### Step 1: Analyze the Assertion
The assertion states that the zeroes of the polynomial \( p(x) = x^3 + 3x^2 - 4x - 12 \) are -2, 2, and 3.

To verify this, we can substitute these values into the polynomial and check if they yield zero.

1. **Substituting -2:**
\[ p(-2) = (-2)^3 + 3(-2)^2 - 4(-2) - 12 = -8 + 12 + 8 - 12 = 0 \]

2. **Substituting 2:**
\[ p(2) = (2)^3 + 3(2)^2 - 4(2) - 12 = 8 + 12 - 8 - 12 = 0 \]

3. **Substituting 3:**
\[ p(3) = (3)^3 + 3(3)^2 - 4(3) - 12 = 27 + 27 - 12 - 12 = 30 \quad (\text{not zero}) \]

Thus, the assertion that the zeroes are -2, 2, and 3 is incorrect because \( p(3) \neq 0 \).

### Step 2: Analyze the Reason
The reason states that the sum of the zeroes is given by \( -\frac{b}{a} \) and the product of the zeroes is given by \( \frac{c}{a} \).

For a cubic polynomial \( ax^3 + bx^2 + cx + d \):
- The sum of the zeroes \( \alpha + \beta + \gamma = -\frac{b}{a} \)
- The product of the zeroes \( \alpha \beta \gamma = -\frac{d}{a} \)

In our case:
- \( a = 1 \), \( b = 3 \), \( c = -4 \), \( d = -12 \)

Calculating the sum of the zeroes:
\[ \text{Sum} = -\frac{3}{1} = -3 \]

Calculating the product of the zeroes:
\[ \text{Product} = -\frac{-12}{1} = 12 \]

### Conclusion
The assertion is incorrect as the zeroes do not match, while the reason is correct in its formula but does not apply correctly to the assertion since it refers to a cubic polynomial instead of a quadratic polynomial.

### Final Answer
- Assertion (A) is **False**.
- Reason (R) is **True** but does not correctly explain (A).