Quadratic Expression that is always negative

Quadratic Expression that is always negative

Secondary 3
  1. Find the range(s) of values of \(k\) if the value of \((k+1){{x}^{2}}+3k-2kx\) is always negative.
  2. Find the range of values of \(k\) for which the expression \(k{{x}^{2}}-8kx+15k-9\) is always negative for all real values of \(x\).

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Answer:(a) \(k<-\frac32\) (b) \(-9<k<0\)

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