If the eqn ax 2 +bx+c=0 (0 1 and Z 2 , then show that |Z 1 | >1 , |Z 2 | >1.

If the eqn ax2+bx+c=0  (0 1 and Z2, then show that |Z1| >1 , |Z2| >1.


2 Answers

Badiuddin askIITians.ismu Expert
148 Points
13 years ago

If the eqn ax2+bx+c=0  (0 <a<b<c) has non real complex roots Z1 and Z2

then z1 & Z2 must be conjugate complex number.

and b2-4ac<0

and |Z1|= |Z2|

so i f  i will prove for one root then it is also true for other root


|z1|=√{b2 +(√(4ac-b2))2}/2a 


        =√(c/a) >1

so |Z1|= |Z2| >1

mycroft holmes
272 Points
13 years ago

As in the previous thread we note that z1 and z2 are complex conjugates. Hence |z1| = |z2|.


Now z1 z2 = c/a and hence |z1 z2| = |z1|2 = |c/a|>1 since c>a>0

Think You Can Provide A Better Answer ?