Question

The condition for ax² + bx+c=0 to be a quadratic equation is

• A. \(a \neq 0, \quad a, b, c \in \mathbb{R}\)
• B. \(a = 0, \quad b = 0, \quad c \neq 0\)
• C. \(a = 0, \quad b \neq 0, \quad c \neq 0\)
• D. \(a=b=c=0\)

Answer 1

The Correct Option is A

Step 1: Definition of a quadratic equation

A quadratic equation is a polynomial equation of degree 2. The general form is: \[ ax^2 + bx + c = 0 \] where \( a, b, c \in \mathbb{R} \) and most importantly, \( a \ne 0 \).

Step 2: Why must \( a \ne 0 \)?

If \( a = 0 \), the equation becomes: \[ 0 \cdot x^2 + bx + c = bx + c = 0 \] which is a linear equation (not quadratic). So, to ensure the term \( x^2 \) exists, \( a \) must not be zero.

Step 3: Role of \( b \) and \( c \)

The values of \( b \) and \( c \) can be zero, non-zero, or any real number. They don’t affect the degree of the equation. Only \( a \ne 0 \) guarantees it is quadratic.

The correct option is (A): \(a \neq 0, \quad a, b, c \in \mathbb{R}\)