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).

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).

cdquestions Admin · Accepted Answer

- 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).

Answer

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

Answer

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

Answer

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

Answer

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

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).

The Correct Option is A

Solution and Explanation

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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).