Answer:
[tex](x-2\sqrt{5}i )(x+2\sqrt{5}i )[/tex]
Step-by-step explanation:
Let solve this first:
[tex]x^2 + 20 = 0\\x^2 = -20\\x = \sqrt{-20} \\x=\sqrt{20}i[/tex]
Note: i = √-1
Using the property of radicals [√a√b=√(ab)], we can write √20 as:
√20 = √4√5 = 2√5
We can write:
x = ± 2√5 i
If we take the two roots (answers) as -a, and a, then we can write the factorization as:
(x - a ) (x + a)
Thus this factorization is:
[tex](x-2\sqrt{5}i )(x+2\sqrt{5}i )[/tex]
