Question

Assertion (A): The polynomial $$x^{2}+4x$$ has two real zeros.

Reason (R): The zeros of the polynomial $$x^{2}+ax\ (a\neq 0)$$ are 0 and $$a$$. 

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

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

Explanation:

Step 1 – Assertion: A is true. Factoring gives $$x^{2}+4x=x(x+4),$$ so its real zeros are $$0$$ and $$-4$$.

Step 2 – Reason: R is false. In general, $$x^{2}+ax=x(x+a),$$ so its zeros are $$0$$ and $$-a,$$ not $$a$$.