2.12: Quadratic equation with √5 coefficients

0606/22/O/N/19 — Question 11 · 6 marks

Do not use a calculator in this question.

(a)
Solve the quadratic equation (5−3)x2+3x+(5+3)=0(\sqrt{5} - 3)x^{2} + 3x + (\sqrt{5} + 3) = 0, giving your answers in the form a+b5a + b\sqrt{5}, where aa and bb are constants.
[6]