How to find roots of a quadratic equation by factorising.
A quadratic equation looks like this:
ax² + bx + c = 0Â (where ‘a’ cannot be zero.)
Solving the equation means finding ‘x’ values that make the equation true. These ‘x’ values are called the roots Â of the quadratic.
Quadratic equations can have 0, 1 or two roots.
In the complex number system, all quadratic equations have roots, but we will
not discuss complex numbers in this article. Roots of quadratics always come in
pairs, but when there are two roots that are the same we say that there is only
This method requires that you can factorise the quadratic expression on the left hand side. This is not always possible, and if not you would have to use one of the other methods.
Consider this quadratic expression...
4x - 5 = 0
When factorised, it looks like this...
(x + 1)(x -
5) = 0
For the example, this means that if (x+1) or (x-5) is zero, the product will be zero and the equation will be true. We use this fact to find the roots as follows:
1 = 0Â soÂ Â Â
5 = 0Â soÂ Â Â
x = 5
Â The example quadratic equation has two roots, x = -1 and x = 5.
Step 1Â Enter the equation to solve
Click Â and type the quadratic equation into the 'maths' box in the data entry dialog box.
If the ‘EMPTY’ message is
not displayed between the blue buttons, click the
until the message: ‘INSERT’ appears. If
required, use the ‘ * ’ symbol for multiply, and the ‘ / ’ symbol for
Â Â Â Â Â Â
Step 2, Solve...
Keep clicking the Â (factorise) button until the equation is factorised, and looks like this:
(x + 1)(x -
5) = 0
If there is a common factor, this will be at the front of the left bracket.
The expressions in brackets must be
equated to zero to find the roots.Â (See
the theory section at the top of this article.)
In this case, x+1 = 0 and x-5
= 0, so the roots are x = -1 and x = 5.
NOTE: If the equation does not factorise, then you will need to use one of the other methods described in the topic: Factorise quadratics.