Maths Core WMA01/WMA02: QUADRATICS Topical Past Paper Questions

The equation $ 2x^{2} + 5px + p = 0 $, where p is a constant, has no real roots. Find the set of possible values for p.

The equation $ 5x^{2} + 6 = k(13x^{2} - 12x) $, where k is a constant, has two distinct real roots. (a) Show that k satisfies the inequality $$ 6k^{2}+13k-5>0 $$ (b) Find the set of possible values for k. (4)