Curve intersection leads to quadratic

A question is this type if and only if finding the intersection points of two curves (e.g. a polynomial and a line) requires setting up and solving a quadratic or disguised quadratic equation.

2 questions · Standard +0.8

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OCR C1 Q5
8 marks Moderate -0.3
  1. Find in exact form the coordinates of the points where the curve \(y = x^2 - 4x + 2\) crosses the \(x\)-axis. [4]
  2. Find the value of the constant \(k\) for which the straight line \(y = 2x + k\) is a tangent to the curve \(y = x^2 - 4x + 2\). [4]
Edexcel AEA 2015 June Q2
9 marks Challenging +1.8
  1. Show that \((x + 1)\) is a factor of \(2x^3 + 3x^2 - 1\) [1]
  2. Solve the equation $$\sqrt{x^2 + 2x + 5} = x + \sqrt{2x + 3}$$ [8]