Multiple choice

Find the roots of following quadratic equation $2x^2\,-\,x\,-\,4\,=\,0$

  1. $\displaystyle\,x\,=\,\frac{2\,\pm\,\sqrt{33}}{4}$
  2. $\displaystyle\,x\,=\,\frac{1\,\pm\,\sqrt{33}}{4}$
  3. $\displaystyle\,x\,=\,\frac{1\,\pm\,\sqrt{33}}{2}$
  4. $\displaystyle\,x\,=\,\frac{1\,\pm\,\sqrt{22}}{4}$
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B Correct answer
Explanation

Using the quadratic formula x = (-b +/- sqrt(b^2 - 4ac)) / 2a. Here a=2, b=-1, c=-4. x = (1 +/- sqrt((-1)^2 - 4*2*(-4))) / (2*2) = (1 +/- sqrt(1 + 32)) / 4 = (1 +/- sqrt(33)) / 4.

AI explanation

Using the quadratic formula for 2x^2 - x - 4 = 0, we get x = (1 plus or minus sqrt(1 + 32)) / 4. This simplifies to x = (1 plus or minus sqrt(33)) / 4.

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