Quadratic equations

There are 39 NRICH Mathematical resources connected to Quadratic equations

problem

Good Approximations

Age

16 to 18

Challenge level

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

problem

Kissing

Age

16 to 18

Challenge level

Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?

problem

Two Cubes

Age

14 to 16

Challenge level

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]

problem

Golden Thoughts

Age

14 to 16

Challenge level

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

article

Golden Mathematics

A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.

article

Continued Fractions II

In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).

interactivity

Proof Sorter - Quadratic Equation

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

Placeholder: several colourful numbers

problem

A third of the area

Age

14 to 16

Challenge level

The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?

problem

Mega Quadratic Equations

Age

14 to 18

Challenge level

What do you get when you raise a quadratic to the power of a quadratic?