Assertion : If `alpha` and `Beta` are the zeroes of the polynomial `x^(2)+2x-15` then `(1)/(alpha)+(1)/(beta)` is `(2)/(15)`.
Reason : If `alpha` and `Beta` are the zeroes of a quadratic polynomial `ax^(2)+bx+c` then `alpha+beta=-(b)/(a)` and `alphabeta=(c)/(a)`

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the assertion and reason provided in the question, we will follow these steps:

### Step-by-step Solution:

1. **Identify the Polynomial**: The polynomial given is \( x^2 + 2x - 15 \).

2. **Identify Coefficients**: From the polynomial \( ax^2 + bx + c \), we can identify:
- \( a = 1 \)
- \( b = 2 \)
- \( c = -15 \)

3. **Calculate the Sum of the Roots (α + β)**: According to the formula for the sum of the roots of a quadratic polynomial:
\[ \alpha + \beta = -\frac{b}{a} \]
Substituting the values:
\[ \alpha + \beta = -\frac{2}{1} = -2 \]

4. **Calculate the Product of the Roots (αβ)**: According to the formula for the product of the roots of a quadratic polynomial:
\[ \alpha \beta = \frac{c}{a} \]
Substituting the values:
\[ \alpha \beta = \frac{-15}{1} = -15 \]

5. **Calculate \( \frac{1}{\alpha} + \frac{1}{\beta} \)**: We can express this as:
\[ \frac{1}{\alpha} + \frac{1}{\beta} = \frac{\beta + \alpha}{\alpha \beta} \]
Substituting the values we found:
\[ \frac{1}{\alpha} + \frac{1}{\beta} = \frac{-2}{-15} = \frac{2}{15} \]

6. **Conclusion**: The assertion states that \( \frac{1}{\alpha} + \frac{1}{\beta} = \frac{2}{15} \), which we have verified to be true. Therefore, the assertion is correct.

7. **Reason Verification**: The reason provided is also correct as it accurately describes the relationships between the coefficients of a quadratic polynomial and its roots.

### Final Answer:
- The assertion is correct, and the reason is the correct explanation of the assertion.