Question

Assertion (A): If the quadratic equation $$px^{2}-4x+4=0$$ has real roots them $$p\leq 1$$.

Reason (R): The quadratic equation $$ax^{2}+bx+c=0$$ has both real 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

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

Explanation:

Step 1 – Assertion: A is true. For real roots, the discriminant must satisfy $$(-4)^{2}-4(p)(4)\geq 0.$$ Therefore $$16-16p\geq 0,$$ so $$p\leq 1.$$

Step 2 – Reason: R is false. A negative discriminant gives no real roots; both roots are real when the discriminant is non-negative.