Quadratic Equations
IGCSE
Edexcel
A quadratic equation is an equation where the highest power of x is 2, usually written in the form ax^2 + bx + c = 0. Solving it means finding the values of x that make the equation true.
Key formulas
\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]
Mistakes students actually make
- Forgetting the \(\pm\) in the quadratic formula.
Worked example
\[\text{Solve } x^2 + 5x + 6 = 0\]
Practice questions
Question 1 - 3 marks
\[\text{Solve } x^2 - 7x + 12 = 0 \text{ by factorising.}\]
\[(x-3)(x-4) = 0\]
\[x = 3 \text{ or } x = 4\]
Common mistake: Forgetting to check that BOTH factors give a valid solution, not just the first one.
Question 2 - 4 marks
\[\text{Solve } 2x^2 + 3x - 2 = 0 \text{ using the quadratic formula.}\]
\[x = \frac{-3 \pm \sqrt{9 + 16}}{4} = \frac{-3 \pm 5}{4}\]
\[x = \frac{1}{2} \text{ or } x = -2\]
Common mistake: Mishandling the sign when squaring a negative b, or losing one solution by dropping the \pm.
Related topics
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