SPS SPS SM 2024 October — Question 4 7 marks

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2024
SessionOctober
Marks7
TopicDiscriminant and conditions for roots
TypeFind range for no real roots
DifficultyStandard +0.3 This is a standard discriminant problem requiring students to apply b²-4ac < 0 for no real roots, then solve a quadratic inequality. While it involves multiple algebraic steps and careful inequality handling, it's a routine application of a core A-level technique with no novel insight required, making it slightly easier than average.
Spec1.02d Quadratic functions: graphs and discriminant conditions1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation

The quadratic equation \(kx^2 + (3k - 1)x - 4 = 0\) has no real roots. Find the set of possible values of \(k\). [7]

The quadratic equation $kx^2 + (3k - 1)x - 4 = 0$ has no real roots. Find the set of possible values of $k$. [7]

\hfill \mbox{\textit{SPS SPS SM 2024 Q4 [7]}}