1.5: Quadratic with surd coefficients (positive root)

0606/12/M/J/16 — Question 4 · 6 marks

Do not use a calculator in this question.

Find the positive value of xx for which (4+5)x2+(2−5)x−1=0(4 + \sqrt{5})x^{2} + (2 - \sqrt{5})x - 1 = 0, giving your answer in the form a+5b\dfrac{a + \sqrt{5}}{b}, where aa and bb are integers.
[6]