Quadratic in disguise, intersection count

A question is this type if and only if it involves a non-standard equation (e.g. involving square roots, reciprocals, or higher-degree substitution) that reduces to a quadratic, and the discriminant is used to determine how many intersection points or real solutions exist.

1 questions · Standard +0.3

Sort by: Default | Easiest first | Hardest first
Edexcel P1 2024 June Q8
7 marks Standard +0.3
  1. The curve \(C _ { 1 }\) has equation
$$y = x \left( 4 - x ^ { 2 } \right)$$
  1. Sketch the graph of \(C _ { 1 }\) showing the coordinates of any points of intersection with the coordinate axes. The curve \(C _ { 2 }\) has equation \(y = \frac { A } { x }\) where \(A\) is a constant.
  2. Show that the \(x\) coordinates of the points of intersection of \(C _ { 1 }\) and \(C _ { 2 }\) satisfy the equation $$x ^ { 4 } - 4 x ^ { 2 } + A = 0$$
  3. Hence find the range of possible values of \(A\) for which \(C _ { 1 }\) meets \(C _ { 2 }\) at 4 distinct points.