Multiple choice

Find the roots of the following quadratic equation $z^2\,+\,6z\,-\,8\,=\,0$

  1. $z\,=\,-3\,\pm\,\sqrt{19}$
  2. $z\,=\,-3\,\pm\,\sqrt{17}$
  3. $z\,=\,-2\,\pm\,\sqrt{17}$
  4. $z\,=\,-3\,\pm\,\sqrt{15}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the quadratic formula z = (-b +/- sqrt(b^2 - 4ac)) / 2a, we get z = (-6 +/- sqrt(36 - 4(1)(-8))) / 2 = (-6 +/- sqrt(36 + 32)) / 2 = (-6 +/- sqrt(68)) / 2 = (-6 +/- 2*sqrt(17)) / 2 = -3 +/- sqrt(17).

AI explanation

Using the quadratic formula, the roots are z = (-6 plus or minus sqrt(36 + 32)) / 2. This simplifies to (-6 plus or minus sqrt(68)) / 2, or (-6 plus or minus 2sqrt(17)) / 2, resulting in z = -3 plus or minus sqrt(17).

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