Two brackets, then each = 0: If a quadratic factorises, write it as two brackets and set each bracket = 0 — because if a product is 0, one of the factors must be 0.
IB-style question — factorise and solve
Solve x² − 5x + 6 = 0.
Step by step
- Two numbers multiply to 6, add to −5: −2 and −3.
- Set each bracket to zero.
Final answer
x = 2 or x = 3.
Get it equal to zero first: Always rearrange to = 0 before factorising. Solving x² = 5x − 6 means first writing x² − 5x + 6 = 0.
Works for every quadratic: When factorising is hard, use the quadratic formula. Read off a, b, c from ax² + bx + c = 0 (with the equation set to zero) and substitute.
IB-style question — use the formula
Solve 2x² + 3x − 1 = 0, giving answers to 3 s.f.
Step by step
- a = 2, b = 3, c = −1.
- Simplify under the root.
Final answer
x = 0.281 or x = −1.78 (3 s.f.).
Mind the signs of a, b, c: A negative c becomes −4ac = +8 here. Bracket every substitution and watch double negatives.
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Make a perfect square, then root: Rewrite as (x − h)² = number, then take the square root of both sides — remembering both signs.
IB-style question — root both sides
Solve (x − 4)² = 9.
Step by step
- Square-root both sides (±).
- Solve each.
Final answer
x = 7 or x = 1.
Don't drop the ±: √9 = 3, but solving (x − 4)² = 9 needs ±3 — otherwise you lose a solution.
On Paper 2, let the GDC solve: On Paper 2, type the quadratic into the GDC's equation solver, or graph it and read the x-intercepts — fastest and least error-prone for messy numbers.
Pick your method
- Factorises nicely? → factorise.
- Asks 'in the form (x−h)²'? → complete the square.
- Messy / 'give to 3 s.f.'? → quadratic formula.
Paper 2 only
- GDC equation solver, or
- graph and read the x-intercepts.
- Always allowed on Paper 2.