Question

Which of the following is a solution of x2 + 2x + 8?

Answer 1

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 $\frac{-b+- \sqrt{b^2-4ac} }{2a}$. We can solve the equation as follows:

$\frac{-b+- \sqrt{b^2-4ac} }{2a} \\ \frac{-2+- \sqrt{2^2-4(1)(8)} }{2(1)} \\ \frac{-2+- \sqrt{4-32} }{2} \\ \frac{-2+- \sqrt{-28} }{2}$
Then we separate the negative from -28 to get:
$\frac{-2+- \sqrt{28}* \sqrt{-1} }{2}=\frac{-2+-2i \sqrt{7} }{2}$
Then we continue to solve by factoring common terms (-2 and 2). We get the solutions of $-1+i \sqrt{7} \\ or \\ -1-i \sqrt{7}$. Choice B matches our first solution.

:)