Quadratic Formula & Equations
Year 10 (IGCSE) 📊 Algebra Solve quadratics using the formula, completing the square.
🔲 Quadratic Equations
A quadratic equation has the form $ax^2 + bx + c = 0$.
Examples: $x^2 - 5x + 6 = 0$, $2x^2 + 3x - 2 = 0$
🔑 The Quadratic Formula
The universal solution for any quadratic:
⚡ Quadratic Formula
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ The discriminant $b^2 - 4ac$ tells you how many solutions: > 0 → two solutions, = 0 → one solution, < 0 → no real solutions.
🔍 Methods of Solving
- Factorisation: Write as $(x+p)(x+q)=0$, then $x=-p$ or $x=-q$
- Quadratic Formula: Works for all quadratics
- Completing the Square: Write as $(x+p)^2 + q = 0$
Factorise: $x^2-5x+6=0 → (x-2)(x-3)=0 → x=2$ or $x=3$
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Interactive Demonstration — Quadratic Formula & Equations
x² Quadratic Equation Solver