Question

Assertion (A): The quadratic equation $$3x^{2}-5x+4=0$$ has no real root.

Reason (R): The equation $$ax^{2}+bx+c=0,\ a\neq 0$$ has no real root, 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 and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. The discriminant is $$(-5)^{2}-4(3)(4)=25-48=-23<0,$$ so the equation has no real roots.

Step 2 – Reason: R is true. A negative discriminant means a quadratic equation has no real roots.

Step 3 – Link: The discriminant of the given equation is negative, so the condition stated in R explains A.