Simplifying the sum of the roots

Level pending

If the only real root of a fifth degree polynomial is \(\frac{1}{3}\), the sum of all roots in simplified form is:

assumptions

  1. \(z_{1}\) and \(z_{2}\) are complex roots;
  2. \(Re_{(z_{1})}\) means the real part of the complex root \(z_{1}\) ;
  3. \(Im_{(z_{1})}\) means the imaginary part of the complex root \(z_{1}\) .
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