Solving a quadratic equation

Part of

Quadratic equations can be solved by the following methods:

- factorising
- graphically
- quadratic formula
- discriminant

Look at the National 4 factorising section before continuing.

When a question asks you to 'solve' a quadratic equation, this means that you are to find the roots of the quadratic. In other words, where does the parabola cut the x-axis?

As a graph cuts the axis when the y coordinate is zero, then we substitute into the quadratic equation and use algebra to solve.

Solve

We need to factorise the trinomial.

When factorised this is .

and are multiplying to give zero, therefore one of these brackets must be equal to zero.

and

Therefore are the roots of quadtratic equations.

Now try the example question below.

- Question
Solve

Factorise the trinomial and then find the two possible values.

Therefore