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Grade: 12
        

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

10 years ago

Answers : (2)

Badiuddin askIITians.ismu Expert
147 Points
							

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,z2={-b±i√(4ac-b2)}/2a

|z1|=√{b2 +(√(4ac-b2))2}/2a 

|z1|=√{b2+4ac-b2}/2a

        =√(c/a) >1

so |Z1|= |Z2| >1



10 years ago
mycroft holmes
272 Points
							

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

10 years ago
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