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Quadratic Functions, Equations and Inequalities - Nature of Roots of Quadratic Equations

Quadratic Functions, Equations and Inequalities - Nature of Roots of Quadratic Equations

IP 3

The curve \(\mathrm{f}(x)=(2k-4){{x}^{2}}+3kx-3\) has a maximum point.

  1. State the range of values of \(k\) for which \(\mathrm{f}(x)\) has a maximum value.
  2. Represent the solution set for values of \(k\) on a number line given that \(\mathrm{f}(x)\) cuts the \(x\)-axis at two distinct points.

Solution:

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Answer:(a) \(k<2\). (b) \(k<-4\) or \(\frac43<k<2\).

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