Paper 22 Q12(b)IGCSE 0580 May/June 2023

Question

One solution of the equation ax^{2}+b=181 is x=8. a and b are both positive integers greater than 1. Write down the other solution of the equation ax^{2}+b=181.

This question tests understanding of quadratic equations and symmetry properties. It's important because recognising patterns in quadratic equations helps solve them more efficiently.

Step-by-Step Solution

Key Takeaway

Quadratic equations of the form ax^2 + b = c have solutions that are equal in magnitude but opposite in sign.

Common Mistakes

Writing +8 instead of -8 because they don't recognise the symmetry property of quadratic equations without linear terms
Trying to work out the values of a and b first, which is unnecessary and wastes time since the symmetry property gives the answer directly

Exam Tip

For quadratic equations with no x term (like ax^2 + b = c), if one solution is positive, the other is always the same number but negative.

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