Factorising is one of the key methods for solving quadratic equations. In this guide, we’ll dive deep into the concept of factorisation, specifically focusing on quadratic equations, to make it easy to understand and apply.
A quadratic equation is an equation of the form ax^2 + bx + c = 0
, where a
, b
, and c
are constants, and x
is the variable we aim to solve for.
Factorising means to rewrite an equation or expression as a product of its factors. In the context of quadratic equations, factorising involves converting the equation into a form (x - p)(x - q) = 0
, where p
and q
are constants. Solving for x
then becomes more straightforward.
There are several methods to factorise a quadratic equation, but we’ll focus on the most common ones:
2x^2 + 4x = 0
can be factorised as 2x(x + 2) = 0
.
(x ± p)^2 = 0
.x^2 + 4x + 4 = 0
can be factorised as (x + 2)^2 = 0
.
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
to find the roots.(x - p)(x - q) = 0
.For x^2 - 3x + 2 = 0
, x = 1, 2
, so it can be factorised as (x - 1)(x - 2) = 0
.
This method is particularly useful for trinomials that can be easily factorised. Here’s how you can use this method:
Consider the equation x^2 + 5x + 6 = 0
.
And there you have it! You’ve successfully factorised the equation using the Regular Quadratic Trinomials Method. This method is generally quick and efficient, especially if you can quickly identify the factor pairs for the constant term.
This method involves turning a quadratic equation into a perfect square trinomial, thus simplifying the solving process.
Once the equation is factorised, solving for x
is simple:
(x - p) = 0
and (x - q) = 0
.x
: x = p
and x = q
.Factorising quadratic equations can seem daunting at first, but it’s a systematic process that gets easier with practice. Knowing how to properly factorise can not only help in solving equations but also aids in understanding the characteristics of different quadratic equations.