Given f(x) = ax² + bx + c, a ≠ 0, b, c ∈ R.

Assertion (A): The factorisation of ax² + bx + c is possible only if its discriminant = b² - 4ac < 0.

Reason (R): To factorise ax² + bx + c, split the coefficient of x into two real numbers such that their algebraic sum is b and their product is ac.

1. Assertion (A) is true, but Reason (R) is false.

2. Assertion (A) is false, but Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Given f(x) = ax² + bx + c, a ≠ 0, b, c ∈ R.

Discriminant (D) = b² - 4ac

We know that,

For D ≥ 0, the equation has real roots so factorisation is possible.

So, assertion (A) is false.

To factorise ax² + bx + c, split the coefficient of x into two real numbers such that their algebric sum is b and their product is ac.

This describes the method of splitting the middle term, which is a valid technique used to factor quadratic expressions over the real numbers — provided real roots exist.

So, reason (R) is true.

Thus, Assertion (A) is false, but Reason (R) is true.

Hence, option 2 is the correct option.