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O-LevelAdditional MathematicsQuadratic functions4037/22 · May/June 2019 · Q24 Marks

Find the values of k for which the equation (k-1)x²+kx-k = 0 has real and distinct roots.

  1. Find the values of k for which the equation (k-1)x²+kx-k = 0 has real and distinct roots.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

  1. [B1] k² - 4(k-1)(-k) oe
  2. [M1] k(5k-4)
  3. [A1] Correct critical values 0, 0.8 oe
  4. [A1] FT their critical values provided their ak² + bk + c > 0 has positive a and there are 2 values; mark final answer. If B1 M0 allow SC1 for a final answer of k > 0.8 oe

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About this question

Topic
Quadratic functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 4 marks.
Source
O-Level Additional Mathematics, May/June 2019 Paper 2 Variant 2, question 2.

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