Question

Factor the expression over the complex numbers. x2+50

Answer 1

  x² + 50

= x² - (-50)

= $\sqrt{x^{2} } +/- \sqrt{-50}$            Side note: $\sqrt{-50} = \sqrt{(-1) * 5 * 5} = 5i$

= (x + 5i)(x - 5i)

Answer 2

Answer:

$(x+5i\sqrt 2)(x-5i\sqrt 2)$

Step-by-step explanation:

We are given that an expression

$x^2+50$

We have to find the factor of given expression over the complex numbers.

Quadratic formula  fro quadratic equation :$ax^2+bx+c=0$

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

Using the formula

$x=\frac{0\pm\sqrt{0-4(50)(1)}}{2}=\frac{\pm i \sqrt{200}}{2}$

$x=\frac{10i\sqrt 2}{2}, x=-\frac{10i\sqrt2}{2}$

$x=5i\sqrt 2, x=-5i\sqrt 2$

$x-5i\sqrt 2=0$  and $x+5i\sqrt 2=0$

Hence, the factor of $x^2+50$ is given by

$(x+5i\sqrt 2)(x-5i\sqrt 2)$