How do you find all the real and complex roots of x^2 + 10x + 26 = 0?

1 Answer
Jul 19, 2018

x = -5+-i

Explanation:

We can complete the square then use the difference of squares identity:

A^2-B^2 = (A-B)(A+B)

with A=(x+5) and B=i as follows:

0 = x^2+10x+26

color(white)(0) = x^2+2(x)(5)+(5)^2+1

color(white)(0) = (x+5)^2-i^2

color(white)(0) = ((x+5)-i)((x+5)+i)

color(white)(0) = (x+5-i)(x+5+i)

Hence:

x = -5+-i