Advanced · 15 min
Solving quadratic equations
Factorise simple quadratics and find both roots.
Find two numbers for the factors
For x² + bx + c, look for two numbers that add to b and multiply to c. This method applies when such factors can be found.
Worked example
x² + 5x + 6 = (x + 2)(x + 3)
Use the zero-product rule
If a product is zero, at least one factor must be zero. Set each factor to zero separately and check every root in the original equation.
Worked example
(x − 4)(x + 1) = 0 gives x = 4 or x = −1.
Find and check both roots
- Solve x² − 5x + 6 = 0 by factorising.
- Substitute both roots into the original equation.