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Janusz Asked

Age 16 to 18
Challenge Level Yellow starYellow star
  • Problem
  • Getting Started
  • Student Solutions
For $y = ax + b$, if you can use the given conditions and write $b$ in terms of $a$, then for any value of $a$ there will be a linear function with this property.

For the second part use the formula relating the sum of the roots and the coefficients and then work systematically to consider all cases.

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Real(ly) Numbers

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

Polynomial Relations

Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one.

More Polynomial Equations

Find relationships between the polynomials a, b and c which are polynomials in n giving the sums of the first n natural numbers, squares and cubes respectively.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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