3.35: Inequality and distinct real roots

0606/23/M/J/22 — Question 4 · 5 marks

(a)
Find the range of values of xx satisfying the inequality (5x1)(6x)<0(5x - 1)(6 - x) < 0.
[2]
(b)
Show that the equation (2k+1)x24kx+(2k1)=0(2k + 1)x^{2} - 4kx + (2k - 1) = 0, where k12k \neq -\tfrac{1}{2}, has distinct real roots.
[3]