A solution of a quadratic equation (ax^2+bx+c) is the point at which the parabola crosses the x-axis. We can find this by using the Quadratic formula, which is [tex] \frac{-b+- \sqrt{b^2-4ac} }{2a} [/tex]. We can solve the equation as follows:
[tex]\frac{-b+- \sqrt{b^2-4ac} }{2a} \\ \frac{-2+- \sqrt{2^2-4(1)(8)} }{2(1)} \\ \frac{-2+- \sqrt{4-32} }{2} \\ \frac{-2+- \sqrt{-28} }{2} [/tex]
Then we separate the negative from -28 to get:
[tex]\frac{-2+- \sqrt{28}* \sqrt{-1} }{2}=\frac{-2+-2i \sqrt{7} }{2}[/tex]
Then we continue to solve by factoring common terms (-2 and 2). We get the solutions of [tex]-1+i \sqrt{7} \\ or \\ -1-i \sqrt{7} [/tex]. Choice B matches our first solution.
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