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Why Two Solutions?
Why Two Solutions?
Quadratic equations have an x² term, which means the graph is a PARABOLA (U-shape). A parabola can cross the x-axis at TWO points, ONE point, or ZERO points. Each crossing point gives you a solution. When we solve by factorising, we're finding where the parabola crosses the x-axis!
The Key Insight
If A × B = 0, then either A = 0 or B = 0 (or both)
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Common Mistakes to Avoid
- WRONG: x² + 5x + 6 = 0 → x = 2 or x = 3 (Forgot the NEGATIVE signs!)
- WRONG: Only writing one answer (Quadratics usually have TWO solutions)
- WRONG: Solving x² + 5x + 6 = 12 by factorising directly (Must rearrange to = 0 first!)
- RIGHT: Always check by substituting BOTH answers back into the original
Now try it yourself
Quiz · Question 1 of 15
The equation x² + 5x + 10 = 0 has:
Tap an answer to check it
This topic in real past papers
Every real exam question we've found on solving quadratics, with a full worked answer.