Factorising Quadratics

If you know the roots x₁ and x₂ of ax² + bx + c, you can write it as a product a(x − x₁)(x − x₂). For example, x² − 5x + 6 has roots 2 and 3, so x² − 5x + 6 = (x − 2)(x − 3). It also works the other way round: from the roots you can build the equation.

What does this generator do?

On the easy level you choose the factorisation of x² + bx + c. On the medium level a ≠ 1 or one root is a fraction, for example 3x² + 4x + 1 = (x + 1)(3x + 1). On the hard level you build equations from roots — whole numbers, fractions or p ± √r.

How to use it

1) Find the roots — with the formula or by finding two numbers with the right sum and product. 2) Write a(x − x₁)(x − x₂) and do not forget a. 3) Watch the signs: the root −3 gives the factor (x + 3). 4) To build an equation, expand a(x − x₁)(x − x₂) and read off the coefficients.