Question

What will be the value of f(x) if, 2A, A + B, C are integers and f(x) = Ax^2 + Bx + C = 0?

(a) Natural Number

(b) Unpredictable

(c) Integer

(d) Complex Number

The question was asked in semester exam.

This intriguing question comes from Applications of Quadratic Equations topic in chapter Complex Numbers and Quadratic Equations of Mathematics – Class 11

Answer 1

Correct choice is (c) Integer

Explanation: f(x) = Ax^2 + Bx + C = 0

So, f(x) = Ax^2 + (A + B)x – Ax + C

              = Ax^2 – Ax + (A + B)x + C

              = 2Ax(x – 1)/2 + (A + B)x + C

Therefore, f(x) is an integer.