Classify the number of real roots of x2+2(m+1)x+m2+1=0 for every real m. State the repeated root whe

Question

Classify the number of real roots of x2+2(m+1)x+m2+1=0 for every real m. State the repeated root when it occurs.

Accepted Answer

Two distinct roots if $m>0$; repeated root $-1$ if $m=0$; none if $m<0$.

Classifying a whole family