Multiple choice

Find the roots of the following quadratic equation $m^2\,-\,3m\,-\,1\,=\,0$

  1. $\displaystyle\,m\,=\,\frac{3\,\pm\,\sqrt{13}}{2}$
  2. $\displaystyle\,m\,=\,\frac{2\,\pm\,\sqrt{13}}{2}$
  3. $\displaystyle\,m\,=\,\frac{3\,\pm\,\sqrt{11}}{2}$
  4. $\displaystyle\,m\,=\,\frac{3\,\pm\,\sqrt{9}}{2}$
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A Correct answer
Explanation

Using the quadratic formula m = [-b +/- sqrt(b^2 - 4ac)] / 2a for m^2 - 3m - 1 = 0: a=1, b=-3, c=-1. m = [3 +/- sqrt((-3)^2 - 4(1)(-1))] / 2 = [3 +/- sqrt(9 + 4)] / 2 = (3 +/- sqrt(13)) / 2.

AI explanation

Using the quadratic formula, the roots are m = (3 plus or minus sqrt((-3)^2 - 4(1)(-1))) / (2 * 1). This becomes (3 plus or minus sqrt(13)) / 2.

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