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