IIT JEE , AIEEE Forum - Mathematics , Algebra

cygnus7

If z₁ and z₂ are the non-real complex roots of ax²+bx+c=0 (0<a<b<c), prove |z₁|>1,|z₂|>1

nitin62225

if this quad. eqn. has complex roots then they will exist in conjugate pairs

so,
let x+iy=z1 nd x-iy=z2 be the two roots

so from here u get the product of roots= c/a >1 (as given)
as the product of roots= (x^2+y^2)>1
so
lz1l,lz2l>1

karthik_abiram

---sorry 4 my silly q--------

budku007

c>a

so c/a is greater than 1

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