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

The Correct Option is A

Step 1: Verifying the assertion:
We are given the polynomial \( p(x) = x^2 - 2x - 3 \). To find its zeroes, we solve the equation \( p(x) = 0 \), or:
\[ x^2 - 2x - 3 = 0 \] We can factor the quadratic equation:
\[ x^2 - 2x - 3 = (x - 3)(x + 1) = 0 \] Thus, the zeroes of the polynomial are \( x = -1 \) and \( x = 3 \). This confirms that Assertion (A) is true.

Step 2: Verifying the reason:
The reason states that the graph of the polynomial intersects the x-axis at (-1, 0) and (3, 0). Since the zeroes of the polynomial are \( x = -1 \) and \( x = 3 \), the graph of the polynomial will indeed intersect the x-axis at these points. This confirms that Reason (R) is true.

Step 3: Conclusion:
Since both Assertion (A) and Reason (R) are true, and Reason (R) explains Assertion (A) completely, the correct answer is:
Both, Assertion (A) and Reason (R) are true. Reason (R) explains Assertion (A) completely.