Solving by quadratic formula - Higher - Solving quadratic equations - Edexcel - GCSE Maths Revision - Edexcel

Solving by quadratic formula - Higher

Using the quadratic formula is another method of solving quadratic equations that will not factorise. You will need to learn this formula, as well as understanding how to use it.

Example

Solve \(x^2 + 6x - 12 = 0\) using the quadratic formula.

First, identify the value of \(a\), \(b\) and \(c\). In this example, \(a = 1\), \(b = 6\) and \(c = -12\).

Substitute these values into the quadratic formula:

\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

\(x = \frac{- 6 \pm \sqrt{6^2 - 4 \times 1 \times -12}}{2 \times 1}\)

\(x = \frac{-6 \pm \sqrt{36 + 48}}{2}\)

\( x = \frac{-6 \pm \sqrt{84}}{2}\)

To calculate the decimal answers, work out each answer in turn on a calculator.

\(x = \frac{-6 \pm \sqrt{84}}{2}\)

The first solution is \(x = \frac{-6 + \sqrt{84}}{2} = 1.58\) (3 sf).

The second solution is \(x = \frac{-6 - \sqrt{84}}{2} = -7.58\) (3 sf).

Question

Solve \(2x^2 - 10x + 3 = 0\) using the quadratic formula.

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Solving quadratic equations - EdexcelSolving by quadratic formula - Higher