O-LevelAdditional MathematicsQuadratic functions4037/11 · May/June 2020 · Q45 Marks

DO NOT USE A CALCULATOR IN THIS QUESTION. Find the positive solution of the equation (5+4√7)x²+(4-2√7)x-1 = 0, giving your answer in the form a+b√7, where a and b are fractions in their simplest form.

(a)DO NOT USE A CALCULATOR IN THIS QUESTION. Find the positive solution of the equation (5+4√7)x²+(4-2√7)x-1 = 0, giving your answer in the form a+b√7, where a and b are fractions in their simplest form.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[M1] For correct use of quadratic formula, allow inclusion of ± until final answer
[M1] For attempt to simplify discriminant, must see attempt at expansion and subsequent simplification
[A1] For either 4+2√7 / (2(5+4√7)) or 2+√7 / (5+4√7)
[M1] For attempt to rationalise, must see attempt at expansion and subsequent simplification
[A1] x = 6/29 + √7/29

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Topic: Quadratic functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source: O-Level Additional Mathematics, May/June 2020 Paper 1 Variant 1, question 4.

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