WHAT IS THE RANGE OF  X^2+3X+5/X^2-5X+4?

Asked by ime_myself23 | 23rd Aug, 2015, 10:54: PM

Expert Answer:

L e t space fraction numerator x squared plus 3 x plus 5 over denominator x squared minus 5 x plus 4 end fraction equals Y rightwards double arrow x squared open parentheses Y minus 1 close parentheses plus x open parentheses negative 5 Y minus 3 close parentheses plus 4 Y minus 5 equals 0 F o r space apostrophe x apostrophe space t o space b e space r e a l comma space D greater or equal than 0 rightwards double arrow open parentheses negative 5 Y minus 3 close parentheses squared minus 4 open parentheses Y minus 1 close parentheses open parentheses 4 Y minus 5 close parentheses greater or equal than 0 rightwards double arrow 25 Y squared plus 9 plus 30 Y minus 4 open parentheses 4 Y squared minus 9 Y plus 5 close parentheses greater or equal than 0 rightwards double arrow 9 Y squared plus 66 Y minus 11 greater or equal than 0 apostrophe a apostrophe space f o r space t h e space a b o v e space q u a d r a t i c space e x p r e s s i o n space i s space p o s i t i v e. R o o t s space o f space t h e space a b o v e space q u a d r a t i c space a r e fraction numerator negative 66 plus-or-minus square root of 66 squared plus 396 end root over denominator 18 end fraction equals fraction numerator negative 11 plus-or-minus square root of 132 over denominator 3 end fraction H e n c e comma space Y element of left parenthesis negative infinity comma space fraction numerator negative 11 minus square root of 132 over denominator 3 end fraction right square bracket space large union space left square bracket fraction numerator negative 11 plus square root of 132 over denominator 3 end fraction comma space infinity right parenthesis

Answered by satyajit samal | 24th Aug, 2015, 11:59: AM