Answer:
[tex]Discriminant=0\\b)\ One\ Real\ Solution[/tex]
Step-by-step explanation:
[tex]We\ are\ given\ that:\\4w^2+8w+4=0\\We\ know\ every\ quadratic\ equation\ can\ be\ represented\ in\ the\ form\ of:\\ax^2+bx+c=0,\ where\ x \neq 0\\Hence,\\Lets\ first\ recognize\ the\ co-efficients\ of\ the\ algebraic\ terms( x^2,\ x,\ x^0),\\ which\ are\ a,b\ and\ c\ respectively.[/tex]
[tex]Hence,\\4w^2+8w+4=0\\4(w^2)+8(w)+4(w^0)=0\\Hence,\\a=4,\ b=8,\ and\ c=4.[/tex]
[tex]Now,\\We\ can\ decide\ the\ nature\ of\ roots\ the\ quadratic\ equation\ has,\ by\ looking\\ at\ its\ Discriminant.\\Hence,\\Lets\ first\ find\ the\ Discriminant\ for\ our\ equation:\\[/tex]
[tex]We\ know\ that,\\Discriminant=b^2-4ac\\\\Substituting\ a=4, b=8, c=4\ in\ the\ Discriminant\ Formula,\ we\ get:\\8^2-4*4*4\\=64-64\\=0\\Hence,\\Discriminant=0[/tex]
[tex]We\ also\ know\ that\ if,\\D>0, The\ equation\ forms\ 2\ distinct\ real\ roots.\\D=0,The\ equation\ forms\ only\ one\ real\ root\ exactly\ at\ the\ x-axis.\\D<0,\ The\ equation\ forms\ Imaginary/Complex\ Roots\ or\ basically\ no\ real\ roots.[/tex][tex]Here,\\As\ D=0,\\The\ equation\ forms\ only\ one\ Real\ root\ or\ has\ only\ one\ solution.[/tex]
