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



 

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