(B) When a=c we obtain ax²+bx+a= 0 which has roots

-b±√(b²-4a²) 2a

And multiplying these two roots together gives b²-(b²-4a²) = 4a²/4a² = 1. 4a²

So the two roots are reciprocals of each other, BUT the Discriminant is not negative unless b²<4a². So |b|<|2a| is required for the roots to be complex (not real roots).

So the first condition would be true if it were |b|<|2a| instead of |b|<|a|.

From this problem we see that there are infinitely many complex number pairs that are complex conjugates AND reciprocals at the same time. But there is only ONE pair of complex numbers that are both OPPOSITES AND RECIPROCALS at the same time. And that would be ...

scientia

2013-01-06 20:20:11

Let the roots be , , , so . Then:

So (i) and (iii) are true.

We have so is true. The others are not necessarily true: e.g. has complex roots and .

jacks

2013-01-06 19:18:46

(A) If all The Roots of the equation

are of unit Modulus then:

Options:

(B) If and The equation has Complex Roots Which are Reciprocal To each other, Then