Complex and quadratic

If the eqn ax²+bx+c=0 (0 < a < b< c) has non real complex roots z₁ and z₂. Show that |z₁| > 1 ; |z₂| > 1.

2 Answers

one thing that can be done is that we can reduce one variable eaisy by dividing by a

we get

x²+(b/a)x+(c/a) = 0

and take b/a as p and c/a as q

then

0 < 1 < p < q

now you have 2 variables

given p² > 4q

now you need to prove that

-pÂ±√p²-4q2 has modulus greater than 1

now you have
|-pÂ±√p²-4q| > 2

but the part inside modulus will be always negative.. (why?)

so this will be same as proving
pÂ±√p²-4q| > 2

p²>4q
and q>1

now then try and use some algebra.. to prove teh result...

thankyou Nishant bhayiya

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