Question

Let Z1 and Z2 be the complex roots of ax^2+bx+c=0 where a≥b≥c>0. Then
a)|z1+z2|≤1
b)|z1+z2|>2
c)|z1|=|z2|=1
d) none

Answer 1

Answer:

Step-by-step explanation:

c is answer

Answer 2

If Z1 and Z2 are the complex roots of ax^2+bx+c=0 where a≥b≥c>0. Then

|z1+z2|>2 (option b).

Given that, we have a quadratic equation

ax^2+bx+c=0 where a≥b≥c>0

the equation has complex roots  Z1 and Z2

We know that in a quadratic equation if one root is a complex number then the other root is the conjugate of the first root.

therefore,

if Z1 = x + iy

then Z2 = x - iy

Now

| Z1 + Z2 | = | x + iy + x - iy|

= | 2x |

We know that x is a real number therefore 2x will be greater than 0

2x > 2

Therefore,  |z1+z2| = 2x > 2