3.2: Quadratic with surd coefficients

0606/12/F/M/22 — Question 2 · 6 marks

Do not use a calculator in this question.

Solve the equation (3−53)x2+(23+5)x−1=0(3-5\sqrt{3})x^{2} + (2\sqrt{3}+5)x - 1 = 0, giving your solutions in the form a+b3a + b\sqrt{3}, where aa and bb are rational numbers.
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