Question

Assertion (A): Zeroes of a polynomial p(x) = x² − 2x − 3 are −1 and 3.

Reason (R): The graph of polynomial p(x) = x² − 2x − 3 intersects x-axis at (−1, 0) and (3, 0).

Options

• Both, Assertion (A) and Reason (R) are true. Reason (R) explains Assertion (A) completely.

• Both, Assertion (A) and Reason (R) are true. Reason (R) does not explain 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. Reason (R) explains Assertion (A) completely.

Explanation:

For the polynomial,

⇒ p(x) = x² − 2x − 3

⇒ p(x) = x² − 3x + x − 3

⇒ p(x) = x(x − 3) + 1(x − 3)

⇒ p(x) = (x − 3)(x − 3)

So, the zeroes are 3 and −1

Also, the graph of given polynomial intersects x-axis at points (3, 0) and (−1, 0)

So, both assertion and reason are true and reason explains assertion completely.