Question

Assertion (A): The polynomial $$p(x)=x^{2}+3x+3$$ has two real zeros.

Reason (R): A quadratic polynomial can have at most two real 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

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

Explanation:

Step 1 – Assertion: A is false. For $$p(x)=x^{2}+3x+3,$$ the discriminant is $$3^{2}-4(1)(3)=9-12=-3<0.$$ Hence, the polynomial has no real zeros.

Step 2 – Reason: R is true. A quadratic polynomial has degree two and can have at most two real zeros.

Step 3 – Link: The fact that a quadratic polynomial can have at most two real zeros does not establish that this particular polynomial has two real zeros.