O-LevelAdditional MathematicsQuadratic functions4037/12 · May/June 2023 · Q25 Marks
DO NOT USE A CALCULATOR IN THIS QUESTION. Solve the equation (2+√5)x² = 4x+3(2-√5), giving your answers in the form a+b√5 where a and b are integers.
- DO NOT USE A CALCULATOR IN THIS QUESTION. Solve the equation (2+√5)x² = 4x+3(2-√5), giving your answers in the form a+b√5 where a and b are integers.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [M1] For attempt to equate to zero and use quadratic formula, must see substitution 4±√16-k / 2(2+√5) and with simplification to 4±√16-k / 2(2+√5)
- [A1] for one exact solution (x = 4±2 / 2(2+√5) or exact equivalent)
- [M1] For evidence of rationalisation and evaluation
- [A1] -6+3√5 and 2 + √5
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