1.11: Parameter inequality for real roots

0606/13/O/N/16 — Question 3 · 6 marks

(i)
Given that 3x2+p(12x)=33x^{2} + p(1 - 2x) = -3, show that, for xx to be real, p23p90p^{2} - 3p - 9 \ge 0.
[3]
(ii)
Hence find the set of values of pp for which xx is real, expressing your answer in exact form.
[3]