SPS SPS SM 2024 October — Question 4

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2024
SessionOctober
TopicInequalities

4. The quadratic equation \(k x ^ { 2 } + 2 k x + 2 k = 3 x - 1\), where \(k\) is a constant, has no real roots.
  1. Show that \(k\) satisfies the inequality $$4 k ^ { 2 } + 16 k - 9 > 0 .$$
  2. Hence find the set of possible values of \(k\). Give your answer in set notation.