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### Number and algebra

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### For younger learners

### Advanced mathematics

# Root to Poly

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### Rudolff's Problem

Links to the University of Cambridge website
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Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 14 to 16

Challenge Level

Find the polynomial $p(x)$ with integer coefficients such that one
solution of the equation $p(x)=0$ is $1+\sqrt{2}+\sqrt{3}$.

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?