Quadratic Formula

**xwrathbringerx** · October 15th 2008, 12:15 AM

Are the solutions to x^2 - 4x - 8 really (4 +/- sqrt(48))/2?

Because everytime I try working it out using the quadratic formula, my answer comes out with a 16 instead of the 4?

??

**mr fantastic** · October 15th 2008, 12:36 AM

Originally Posted by xwrathbringerx

Are the solutions to x^2 - 4x - 8 really (4 +/- sqrt(48))/2?

Because everytime I try working it out using the quadratic formula, my answer comes out with a 16 instead of the 4?

??

Yes.

$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-8)}}{2} = \frac{4 \pm \sqrt{16 + 32}}{2} = \frac{4 \pm \sqrt{48}}{2}$

Note: $= \frac{4 \pm \sqrt{16 \times 3}}{2} = \frac{4 \pm 4 \sqrt{3}}{2} = 2 \pm 2 \sqrt{3}$ .

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