Solving Quadratics by Factorising
How do I solve simple quadratic equations?
- If the equation is of the form , there is an term that is equal to a constant
- First divide both sides by and then take the square root
- For example,
How do I solve a quadratic equation using factorisation?
- If a quadratic equation includes an term, then you will need to factorise the equation in order to solve it
- Factorise the quadratic
- E.g.
- Set each bracket to zero and solve for
- Because if A × B = 0, then either A = 0 or B = 0
- For the first bracket
- For the second bracket
- The two solutions are and
- To solve a quadratic that factorises to a single bracket with a variable outside
- E.g.
- For the first bracket, it may help to think of as
- For the second bracket
- The two solutions are and
- It is a common mistake to divide both sides by at the beginning - you will lose a solution (the solution)
Exam Tip
- Use a calculator to check your final solutions!
- Calculators also help you to factorise (if you're struggling with that step).
Worked example
Solve
Set the first bracket equal to zero
x – 2 = 0
Add 2 to both sides
x = 2
Set the second bracket equal to zero
x + 5 = 0
Subtract 5 from both sides
x = -5
Write both solutions together using “or”
x = 2 or x = -5
Solve
Do not divide both sides by x (this will lose a solution at the end)
Set the first “bracket” equal to zero
(x) = 0
Solve this equation to find x
x = 0
Set the second bracket equal to zero
5x - 1 = 0
Add 1 to both sides
5x = 1
Divide both sides by 5
x =
Write both solutions together using “or”
x = 0 or x =