Solving Quadratics
What you’ll learn
- How to recognise a quadratic expression.
- How to factorise quadratics like x² + bx + c into two brackets.
- How to solve a quadratic equation once it is factorised.
1. What is a quadratic?
A quadratic is an expression or equation where the highest power of the variable is squared, such as x² or a².
Definition
Quadratic
A quadratic expression has a squared term as its highest power, for example x² + 5x + 6.
2. Factorising x² + bx + c
For quadratics like x² + bx + c, you are looking for two numbers that:
- multiply to make the constant term, c
- add to make the coefficient of the x-term, b
Example
Factorising with two positive signs
- Factorise x² + 6x + 8.
- Find two numbers that multiply to 8 and add to 6. The pair is 2 and 4.
- Put those numbers into brackets with x:x² + 6x + 8 = (x + 2)(x + 4)
- Check the middle term: 2x + 4x = 6x, so the factorisation works.
Common Mistake
Only checking the multiply part
For x² + 6x + 8, the numbers must multiply to 8 and add to 6. The pair 1 and 8 multiplies to 8, but adds to 9, so it is not correct.
