Solving quadratic equations

Quadratic equations can be solved by the following methods:

factorising
graphically
quadratic formula
discriminant

Factorising

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 \(y = 0\) into the quadratic equation and use algebra to solve.

Example

Solve \({x^2} - 9x + 20 = 0\)

We need to factorise the trinomial.

When factorised this is \((x - 4)(x - 5) = 0\).

\((x - 4)\) and \((x - 5)\) are multiplying to give zero, therefore one of these brackets must be equal to zero.

\((x - 4) = 0\)

\(x = 0 + 4\)

\(x = 4\)

and

\((x - 5) = 0\)

\(x = 0 + 5\)

\(x = 5\)

Therefore \(x = 4\,and\,x = 5\) are the roots of quadtratic equations.

Now try the example question below.

Question

Solve \({x^2} + x - 6\)

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Solving a quadratic equationSolving quadratic equations