Question

Assertion (A): The quadratic equation $$x^{2}-4x+3=0$$ has both real roots.

Reason (R): The equation $$ax^{2}+bx+c=0,\ a\neq 0$$ has both real roots, if $$(b^{2}-4ac)\geq 0$$.

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 and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. The discriminant is $$(-4)^{2}-4(1)(3)=16-12=4>0,$$ so the equation has two real roots.

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

Step 3 – Link: The equation’s discriminant is positive, so the condition in R directly establishes A.