Quadratic equations

  • Erratic quadratic
    problem

    Erratic Quadratic

    Age
    16 to 18
    Challenge level
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    Can you find a quadratic equation which passes close to these points?

  • Quad solve
    problem

    Quad Solve

    Age
    16 to 18
    Challenge level
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    Can you solve this problem involving powers and quadratics?

  • Target Six
    problem

    Target Six

    Age
    16 to 18
    Challenge level
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    Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.

  • Golden Ratio
    problem

    Golden Ratio

    Age
    16 to 18
    Challenge level
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    Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.

  • Purple crocuses in the snow.
    problem

    Polar Flower

    Age
    16 to 18
    Challenge level
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    This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.

  • Plus or Minus
    problem

    Plus or Minus

    Age
    16 to 18
    Challenge level
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    Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.

  • Golden Mathematics
    article

    Golden Mathematics

    A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.
  • Continued Fractions II
    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/...)).