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Polynomials, Cubic Equations and Partial Fractions - Cubic Expressions and Equations

Polynomials, Cubic Equations and Partial Fractions - Cubic Expressions and Equations

TGM Original Questions
  1. Solve the equation \(2x^{2} - 9x + 3 = -\frac{4}{x}\).
  2. Based on your answer in (i), solve the equation
    \(2 \cot\left(\frac{4}{3}x\right) - 9 + 3 \tan\left(\frac{4}{3}x\right) = -4 \tan^{2}\left(\frac{4}{3}x\right), \text{ for}\hspace{0.5em} 0 \le x \le 1.\)

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Answer:(i) \(x = 1, 4, -\dfrac{1}{2}\); (ii) \(x = \dfrac{3\pi}{16}\) or \(0.184\) rad

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