To solve a quadratic equation, first make one side equal to 0. Then factorise. If two brackets multiply to give 0, one of them must be 0. So (x − 5)(x + 3) = 0 gives x = 5 or x = −3.
Rearrange first if you need to: x² = −15x − 56 becomes x² + 15x + 56 = 0, which factorises to (x + 7)(x + 8) = 0, so x = −7 or x = −8. If every term has a common factor, divide it out first: 3x² − 24x + 45 = 0 becomes x² − 8x + 15 = 0.
Worked example
Solve x² − 2x − 15 = 0
- Factorise: (x − 5)(x + 3) = 0.
- Set each bracket to zero.
Answer:x = 5 or x = −3
Key words
- root
- a solution of the equation
- zero product
- if ab = 0 then a = 0 or b = 0
- quadratic equation
- an equation with x²
Practise this
New questions every time.
Common Core-referenced: HSA-REI.B.4b