Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Janusz Asked

## You may also like

### Real(ly) Numbers

### Polynomial Relations

### More Polynomial Equations

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 16 to 18

Challenge Level

- 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.

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

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?

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.

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.