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

1 Answer
Jul 19, 2018

Answer:

#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#