Question

Assertion (A): The polynomial $$p(x)=(x^{3}+x)$$ has one real zero.

Reason (R): A polynomial of nth degree has at most n zeros.

Options

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

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

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

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

Explanation:

Both statements are true.

To identify the real zero, factor the polynomial:

$$x^{3}+x=x(x^{2}+1)$$

For real $$x$$, $$x^{2}+1>0$$, so the only real zero is $$x=0$$. The Reason states only that a cubic polynomial has at most three zeros; this does not explain why this polynomial has exactly one real zero.