Edexcel C12 2016 January — Question 13

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2016
SessionJanuary
TopicQuadratic Functions
13. The equation \(k \left( 3 x ^ { 2 } + 8 x + 9 \right) = 2 - 6 x\), where \(k\) is a real constant, has no real roots.
  1. Show that \(k\) satisfies the inequality $$11 k ^ { 2 } - 30 k - 9 > 0$$
  2. Find the range of possible values for \(k\).
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