O-LevelAdditional MathematicsQuadratic functions4037/22 · May/June 2021 · Q35 Marks
Find the values of the constant k for which (2k-1)x² +6x+k+1 = 0 has real roots.
- Find the values of the constant k for which (2k-1)x² +6x+k+1 = 0 has real roots.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- M1 Uses b²-4ac: 6²-4(2k-1)(k + 1)
- M1 dep on first M1 -8k²-4k+40 * 0 oe where * is = or any inequality sign condone one sign or arithmetic slip in simplification
- M1 Factorises or solves their 3-term quadratic expression or equation for CVs e.g. (5+2k)(8-4k) oe
- A1 Finds correct CVs: -2.5 oe, 2
- A1 mark final answer -2.5 ≤ k ≤ 2
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