Question 465252
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi,
Use the rational root theorem
IF f(x)=x^2+2x+1 = 0  Green
(x+1)(x+1)=0  |x = -1 is the single rational solution

IF f(x)=x^2-2x+5 = 0   Blue
(x-1)^2 + 4 =0 Completing the square
|x = 1 ± 2i  NO rational roots

IF f(x)=x^2+4x-5 = 0   Purple
(x+5)(x-1)= 0 
(x+5)= 0
   x = -5
(x-1)= 0  
   x = 1
x = -5 and x = 1 are the rational solutions
{{{drawing(300,300,   -6, 6, -6, 6, grid(1),
graph( 300, 300, -6, 6, -6, 6,0,x^2+2x+1,x^2-2x+5,x^2+4x-5))}}}