Multiple choice

Which of the following option is the standard form of the mentioned quadratic equation? $2z\, -\,\displaystyle \frac{5}{z}\, =\, z\, -\, 6$

  1. $z^{2}\, +\, 6z\, =\, 0$
  2. $z^{2}\, -\, 6z\, -\, 5\, =\, 0$
  3. $z^{2}\, +\, 6z\, -\, 5\, =\, 0$
  4. $z^{2}\, +\, 6z\, +\, 5\, =\, 0$
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C Correct answer
Explanation

Starting with 2z - 5/z = z - 6, multiply by z to get 2z^2 - 5 = z^2 - 6z. Rearranging gives z^2 + 6z - 5 = 0.

AI explanation

Multiply the entire equation by z to eliminate the fraction, which gives 2z^2 - 5 = z^2 - 6z. Rearranging all terms to one side sets the equation to zero: 2z^2 - z^2 + 6z - 5 = 0. Combining the like terms results in the standard form z^2 + 6z - 5 = 0.

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