Paper 22 Q12(a)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. Find the value of b.

This question tests your ability to substitute values into algebraic expressions and use factor pairs to find unknown values. It combines algebraic manipulation with number theory skills.

Step-by-Step Solution

Key Takeaway

When you have one solution to a quadratic equation, substitute it to create a simpler equation with fewer unknowns.

Common Mistakes

Forgetting that both a and b must be positive integers greater than 1, leading to accepting invalid solutions
Not checking whether the calculated value of b satisfies all the given conditions before writing the final answer

Exam Tip

Always check your answer by substituting back into the original equation to verify it works.

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