How do you find all the real and complex roots of #x^2 + 10x + 26 = 0#?
1 Answer
Jul 19, 2018
Explanation:
We can complete the square then use the difference of squares identity:
#A^2-B^2 = (A-B)(A+B)#
with
#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#
