Quadratic formula practice questions

The quadratic formula solves any equation of the form ax squared plus bx plus c equals 0, giving x equals minus b plus or minus the square root of b squared minus 4ac, all over 2a. Work out the discriminant first, then substitute carefully using brackets around any negative values.

The quadratic formula solves any quadratic equation, including those that will not factorise. For ax² + bx + c = 0, the solutions are x = (−b ± √(b² − 4ac)) ÷ 2a.

The method, step by step

1. Rearrange to equal zero. The formula only works when one side is 0.
2. Identify a, b and c. Include the signs. A common slip is dropping a negative.
3. Work out the discriminant first. Calculate b² − 4ac before anything else.
4. Substitute carefully. Use brackets around negative values.
5. Split into two answers. The ± gives one solution using + and one using −.

Worked example

Common mistakes

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