Assertion (A ) : the number of roots of `x^4 +2x^3 -7x^2 -8x +12=0`
Reason (R ) : Every algebraic equation of degree n has n roots and nomore .

Options

A. both A and R are true R is the correct explanation of A
B. both A and R are true and R is not correct explanation of A
C. A is true and R is false
D. A is false and R is true

Answer

To solve the given question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
The assertion states that the number of roots of the polynomial equation \(x^4 + 2x^3 - 7x^2 - 8x + 12 = 0\) is less than 4.

2. **Understanding the Reason (R)**:
The reason states that every algebraic equation of degree \(n\) has \(n\) roots and no more. This is a fundamental theorem in algebra, which tells us that a polynomial of degree \(n\) will have exactly \(n\) roots, counting multiplicities.

3. **Degree of the Polynomial**:
The polynomial given is of degree 4 (the highest power of \(x\) is 4). According to the reason, this means that the polynomial can have exactly 4 roots.

4. **Analyzing the Assertion**:
Since the polynomial is of degree 4, it must have exactly 4 roots (including real and complex roots, and counting multiplicities). Therefore, the assertion that the number of roots is less than 4 is incorrect.

5. **Conclusion**:
- Assertion (A) is false because the polynomial has exactly 4 roots.
- Reason (R) is true because it correctly states that a polynomial of degree \(n\) has \(n\) roots.

Thus, the final conclusion is:
- Assertion (A) is false.
- Reason (R) is true.
- The reason is not the correct explanation of the assertion.

### Final Answer:
- Assertion (A) is false.
- Reason (R) is true.