Question

Which of the following is a solution of x^2 + 2x + 4?

Answer 1

Answer:

$\displaystyle x_1=-1+\sqrt{3}i$

$\displaystyle x_2=-1-\sqrt{3}i$

Step-by-step explanation:

Second-Degree Equation

The second-degree equation or quadratic equation has the general form

$ax^2+bx+c=0$

where a is non-zero.

There are many methods to solve the equation, one of the most-used is by using the solver formula:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The equation of the question has the values: a=1, b=2, c=4, thus the values of x are

$\displaystyle x=\frac{-2\pm \sqrt{2^2-4\cdot 1\cdot 4}}{2\cdot 1}$

$\displaystyle x=\frac{-2\pm \sqrt{-12}}{2}$

Since the square root has a negative argument, both solutions for x are imaginary or complex. Simplifying the radical

$\displaystyle x=\frac{-2\pm 2\sqrt{-3}}{2}=-1\pm\sqrt{3}i$

The solutions are

$\displaystyle x_1=-1+\sqrt{3}i$

$\displaystyle x_2=-1-\sqrt{3}i$