Higher Tier2.7 Quadratic EquationsPapers 1H & 2H
Solving Quadratics — The Root Finder
Master three methods: Factorising, Quadratic Formula, and Completing the Square.
🎯The Root Finder
Two Real RootsDiscriminant: b² - 4ac = 16
Vertical Shift+0
x² - 4 = 0
Drag to shift the parabola up/down — watch the roots appear and disappear!
📡Logic Track
The Zero Product Rule
If A × B = 0, then either A = 0 or B = 0. That is why we set each bracket to zero and solve.
Factorisable!
(x - 2)(x + 2) = 0
So x = 2 or x = -2
⚡Dynamic SolverSolve 3x² - x - 5 = 0 (2 d.p.)
Step 1: Identify a, b, c
3x² - x - 5 = 0
a = 3, b = -1, c = -5
⚠Examiner Trap Alert
Trap 1: Forgetting the ± in the quadratic formula — this gives you only ONE root instead of two. Instant loss of 1-2 marks.
Trap 2: Writing x = 2, 3 instead of x = 2 or x = 3. The examiner wants the word "or" between your solutions.
Trap 3: Not rearranging to = 0 first. If the question gives x² + 3x = 5, you MUST rewrite as x² + 3x - 5 = 0 before factorising or using the formula.