Question

Assertion (A): The quadratic equation $$\sqrt{3}x^{2}+11x+6\sqrt{3}=0$$ has both real roots.

Reason (R): The quadratic equation $$ax^{2}+bx+c=0$$ has both imaginary roots, if $$(b^{2}-4ac)<0$$.

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:

Step 1 – Assertion: A is true. The discriminant is $$11^{2}-4(\sqrt{3})(6\sqrt{3})=121-72=49>0,$$ so the equation has two real roots.

Step 2 – Reason: R is true. A negative discriminant gives non-real (imaginary) roots.

Step 3 – Link: R describes the condition for imaginary roots; it does not explain why the given equation has real roots.