Question

Assertion (A): The quadratic equation $$x^{2}+3x+4=0$$ 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

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

Explanation:

Step 1 – Assertion: A is false. For the equation, $$a=1,\ b=3,\ c=4.$$ Its discriminant is $$b^{2}-4ac=3^{2}-4(1)(4)=9-16=-7<0,$$ so it does not have real roots.

Step 2 – Reason: R is true. A quadratic equation has real roots when its discriminant is non-negative.

Step 3 – Link: Since A is false, R cannot explain it.