Moderate -0.3 This is a standard discriminant problem requiring students to set the equations equal, form a quadratic, and apply b²-4ac > 0. While it involves multiple algebraic steps and careful manipulation, it's a routine A-level technique with no novel insight required. The 6 marks reflect working rather than conceptual difficulty, making it slightly easier than average.
In this question you must show detailed reasoning.
A curve has equation
$$y = 2x^2 + px + 1$$
A line has equation
$$y = 5x - 2$$
Find the set of values of \(p\) for which the line intersects the curve at two distinct points.
Give your answer in exact form using set notation. [6]
In this question you must show detailed reasoning.
A curve has equation
$$y = 2x^2 + px + 1$$
A line has equation
$$y = 5x - 2$$
Find the set of values of $p$ for which the line intersects the curve at two distinct points.
Give your answer in exact form using set notation. [6]
\hfill \mbox{\textit{SPS SPS SM 2023 Q4 [6]}}