Original Maiths practice · Edexcel IGCSE Maths
Solve x² − 2x − 15 = 0
Find every real value of x that satisfies x² − 2x − 15 = 0. Try factorising first, then verify both solutions by substitution. This is an original Maiths practice question, with no official mark allocation.
Step-by-step solution
- The constant term is −15, so the two integers must have opposite signs. List pairs with product −15: 1 and −15, −1 and 15, 3 and −5, or −3 and 5.
- The required sum is −2. Choose 3 and −5 because 3 + (−5) = −2. This gives (x + 3)(x − 5) = 0.
- A product can equal zero only if at least one factor equals zero. Solve x + 3 = 0 and x − 5 = 0 separately to obtain x = −3 or x = 5.
Check the answer
For x = −3, the left side is 9 + 6 − 15 = 0. For x = 5, it is 25 − 10 − 15 = 0. Both roots work, so neither should be discarded.
Common errors
If your answers are 3 and −5, you identified the numbers inside the brackets but did not solve the two linear equations. If you only wrote the brackets, the factorisation is correct but the request to solve is unfinished.
Extend your understanding
If the question instead asked where y = x² − 2x − 15 crosses the x-axis, report the points (−3, 0) and (5, 0). The roots describe x-values; coordinates describe positions on a graph.
Skill and difficulty
Skill: Quadratic equations by factorising. This is a method-practice question: attempt it after learning the corresponding topic, then use the extension to check deeper understanding. This learning label is not an official examination grade.
Related resources
Content updated: .