2.18: Quadratic equation with √7 coefficients

0606/23/O/N/20 — Question 11 · 7 marks

Do not use a calculator in this question.

(a)
Solve the quadratic equation (7−2)x2−4x+(7+2)=0(\sqrt{7} - 2)x^{2} - 4x + (\sqrt{7} + 2) = 0, giving each of your answers in the form a+b7a + b\sqrt{7}, where aa and bb are constants.
[7]