The curve with equation y=px2−2px−4py = px^2 - 2px - 4py=px2−2px−4p, where p p\,p is a constant does not intersect the line with equation y=2x−7y = 2x - 7y=2x−7.
Show that 5p2−5p+1<05p^2 - 5p + 1 < 05p2−5p+1<0
Find the set of possible values for ppp.
Hence find the set of possible values for 1p\displaystyle \frac{1}{p}p1.
206 exam-style questions on Edexcel A Level Maths Equations and Inequalities, covering 3.1 Linear Simultaneous Equations, 3.2 Quadratic Simultaneous Equations, 3.3 Simultaneous Equations on Graphs, 3.4 Linear Inequalities, 3.5 Quadratic Inequalities, and 3.6 Inequalities on Graphs. Each one has a worked solution and a mark scheme showing where the marks go.