[Solution] (a) Solve the equation 12 x^3-4 x^2-5 x+2=0 given that it has a repeated root. (b) If α, β, γ are roots of the equation a x^3+b
Question: (a) Solve the equation \(12 x^{3}-4 x^{2}-5 x+2=0\) given that it has a repeated root.
(b) If \(\alpha, \beta, \gamma\) are roots of the equation \(a x^{3}+b x^{2}+c x+d=0\), determine the equation whose roots are \(\alpha^{2}, \beta^{2}\), and \(\gamma^{2}\).
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[Solution] Determine the derivatives of the following functions:
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