Question

Assertion (A): The polynomial p(y) = y² + 4y + 3 has two zeroes.

Reason (R): A quadratic polynomial can have at most two zeroes.

Options

• Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

• Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

Explanation:

The polynomial p(y) = y² + 4y + 3 has two zeroes.

y² + 4y + 3 = 0

y² + 3y + y + 3 = 0

y(y + 3) + 1(y + 3) = 0

(y + 3)(y + 1) = 0

y + 3 = 0 or y + 1 = 0

y = −3 or y = −1

We find it has exactly two zeroes (−3 and −1).

This directly matches the rule that a quadratic polynomial can have at most two zeroes.

Since the assertion is a specific example of the general rule stated in the reason, (R) is the correct explanation for (A).