Prove that equation cannot have complex roots

Show that the equation A²x-a+ B²x-b+....+H²x-h=x+Î» where A,B,C...a,b,c...Î» are real numbers,cannot have complex roots.

2 Answers

This is kind of simple...

Lets assume complex roots... as a1+ib1, a2+ib2,....

then substitute for x , a1+ib1

then a1-ib1 will also be a root

now take the difference.. / sum ...

Complete the rest of the proof yourself...

Another method

wlog, assume a< b< c< ....< h

See if there is a root between a, b
between b and c and so on.....

and also between -infinity and a

also betweeen h and + infinity...

What is the max no of roots of this given equation?

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