Quadratic equations

problem
Always two

Age

14 to 18

Challenge level

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
problem
How many balls?

Age

16 to 18

Challenge level

A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.
problem
Halving the triangle

Age

16 to 18

Challenge level

Draw any triangle PQR. Find points A, B and C, one on each side of the triangle, such that the area of triangle ABC is a given fraction of the area of triangle PQR.
problem
In between

Age

16 to 18

Challenge level

Can you find the solution to this algebraic inequality?
problem
Implicitly

Age

16 to 18

Challenge level

Can you find the maximum value of the curve defined by this expression?
problem
Erratic quadratic

Age

16 to 18

Challenge level

Can you find a quadratic equation which passes close to these points?
problem
Quad solve

Age

16 to 18

Challenge level

Can you solve this problem involving powers and quadratics?
problem
Golden ratio

Age

16 to 18

Challenge level

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.
problem
Polar flower

Age

16 to 18

Challenge level

This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.