Multiple choice

Find the roots of the following quadratic equation $x\,(x\,-\,1)\,=\,1$

  1. $\displaystyle\,x\,=\,\frac{1\,\pm\,\sqrt5}{2}$
  2. $\displaystyle\,x\,=\,\frac{2\,\pm\,\sqrt5}{2}$
  3. $\displaystyle\,x\,=\,\frac{3\,\pm\,\sqrt5}{2}$
  4. $\displaystyle\,x\,=\,\frac{4\,\pm\,\sqrt5}{2}$
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A Correct answer
Explanation

x^2 - x - 1 = 0. Using quadratic formula: x = (-b +/- sqrt(b^2 - 4ac)) / 2a = (1 +/- sqrt(1 - 4(1)(-1))) / 2 = (1 +/- sqrt(5)) / 2.

AI explanation

Expanding x(x - 1) = 1 yields the quadratic equation x^2 - x - 1 = 0. Using the quadratic formula, the roots are x = (1 plus or minus sqrt(1 + 4)) / 2, resulting in x = (1 plus or minus sqrt(5)) / 2.

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