This is a Test of Mathematics Solution Subjective 73 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta
Consider the equation , where G and H are complex numbers. Suppose that this equation has a pair of complex conjugate roots. Show that both G and H are real.
Let three roots of the equation are
[ Let
are complex conjugates] .Now
= - H ... (i)
= 0 ... (ii)
= G ... (iii)
From (ii) we get
= 0 [ are complex conjugates so they are real]
= real Now as
= real
=
=
=
... (iv)
are complex conjugates so
... (v) From (iv) & (v) we get
=
G = real [from (iii)] Now
is real and
is real so
= real
H = real.
This is a Test of Mathematics Solution Subjective 73 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta
Consider the equation , where G and H are complex numbers. Suppose that this equation has a pair of complex conjugate roots. Show that both G and H are real.
Let three roots of the equation are
[ Let
are complex conjugates] .Now
= - H ... (i)
= 0 ... (ii)
= G ... (iii)
From (ii) we get
= 0 [ are complex conjugates so they are real]
= real Now as
= real
=
=
=
... (iv)
are complex conjugates so
... (v) From (iv) & (v) we get
=
G = real [from (iii)] Now
is real and
is real so
= real
H = real.