0606/22 May/Jun 2026, Question 2: The Discriminant and Nature of Roots
Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 3 marks
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The question, in short
Show that no real value of k makes the quadratic (k − 2)x² + (2k + 3)x + 3 = 0 have two equal roots.
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Solution · 3 marks
- 1Equal roots need b² − 4ac = 0
- 2(2k + 3)² − 4(k − 2)(3) = 4k² + 12k + 9 − 12k + 24
- 3= 4k² + 33
- 44k² + 33 = 0 gives k² = −33/4, impossible for real k
- 5So there is no real k for which the roots are equal
AnswerDiscriminant = 4k² + 33; 4k² + 33 = 0 has no real solution, so no real k gives equal roots shown
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Also searched as: 0606/22/M/J/26 · 0606_s26_qp_22 · 0606 s26 22 · question 2.
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