What is a quadratic equation?

Definition

A quadratic equation is an equation of the form:

ax^2 + bx + c = 0

where a, b and c are real numbers, with the essential condition that a ≠ 0 (otherwise it is no longer a quadratic equation but a linear equation).

Identifying the coefficients

Identifying a, b and c is the first step before solving the equation.

Equation	a	b	c
2x² - 5x + 3 = 0	2	-5	3
x² - 4 = 0	1	0	-4
-3x² + x = 0	-3	1	0

Common pitfall

Be careful with the sign: in 3x² - 7x + 2 = 0, the coefficient b is -7, not 7. A mistake with the sign here will throw off the entire calculation of the discriminant later on.

Why is a ≠ 0?

If a = 0, the x² term disappears and the equation becomes bx + c = 0, a first-degree equation with at most one solution. A quadratic equation is characterised precisely by the presence of the x² term, which allows for up to two solutions.

This chapter lays the foundations: correctly identifying the coefficients is essential for applying the discriminant formulas correctly, as covered in the next lesson.