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O-LevelAdditional MathematicsQuadratic functions4037/22 · May/June 2022 · Q35 Marks

Find the possible values of k for which the equation kx² + (k+5)x-4 = 0 has real roots.

  1. Find the possible values of k for which the equation kx² + (k+5)x-4 = 0 has real roots.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

  1. [M1] Uses b²-4ac oe: (k+5)² - 4k(-4) [* 0, where * could be = or any inequality sign]
  2. [A1] Forms a correct 3-term expression: k² + 26k +25
  3. [M1] Factorises k² + 26k + 25 or solves k² + 26k + 25 = 0 oe dep on first M1, FT their 3-term quadratic in k
  4. [A1] Correct critical values -1, - 25 soi
  5. [A1] k≤-25, k≥-1 mark final answer

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About this question

Topic
Quadratic functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, May/June 2022 Paper 2 Variant 2, question 3.

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