Do not use a calculator in this question. Find the positive value of x for which (4 + √5)x² + (2 - √5)x - 1 = 0, giving your answer in the form (a + √5) / b, where a and b are integers.

Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

1. [1] M1 for use of quadratic formula (allow one sign error), allow b² = 9-4√5
2. [1] A1 all correct
3. [1] DM1 for attempt to simplify the discriminant (minimum of 4 terms must be seen in discriminant, 2 terms involving √5 and 2 constant terms)
4. [1] A1 for (3+√5)/(2(4+√5)) or (3+√5)/(8+2√5), ignore negative solution if included
5. [1] M1 for attempt to rationalise an expression of the form (a+b√5)/(c±d√5) as part of their solution of the quadratic Must obtain an integer denominator
6. [1] A1 Final A1 can only be awarded if all previous marks have been obtained