Question

Assertion (A): Zeroes of a polynomial $p(x) = x^2 − 2x − 3$ are -1 and 3.
Reason (R): The graph of polynomial $p(x) = x^2 − 2x − 3$ intersects the x-axis at (-1, 0) and (3, 0).

• A. Both, Assertion (A) and Reason (R) are true. Reason (R) explains Assertion (A) completely.
• B. Both, Assertion (A) and Reason (R) are true. Reason (R) does not explain Assertion (A).
• C. Assertion (A) is true but Reason (R) is false.
• D. Assertion (A) is false but Reason (R) is true.

Answer 1

Answer: (A)

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

Answer 2

- The given polynomial is $p(x) = x^2 - 2x - 3$. To find the zeroes, we solve $x^2 - 2x - 3 = 0$ by factoring:

$x^2 - 2x - 3 = (x - 3)(x + 1) = 0$

Thus, the zeroes of the polynomial are $x = 3$ and $x = -1$.

- The graph of a quadratic polynomial intersects the $x$-axis at its zeroes. Therefore, the points where the graph intersects the $x$-axis are $(-1, 0)$ and $(3, 0)$, as given in the reason.

Since both the assertion and the reason are true, and the reason explains the assertion, the correct answer is (a).