CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let x1,x2 are the roots of the quadratic equation x2+ax+b=0 where a,b are complex numbers and y1,y2 are the roots of the quadratic equation y2+ay+b=0. If x1=x2=1 then prove that y1=y2=1

Open in App
Solution

Suppose x2+ax+b=0 has root x1 x2. Then,
x1+x2=a
and
x1x2=b
From (2),

|x1||x2|=|b|
|b|=1
Also,

|a|=|x1+x2|

|a||x1|+|x2|

or

|a|2

Now suppose y2+|a|y+|b|=0 has roots y1 and y2 Then,

y1=y2=|a|±|a|24|b|2

=|a|±(4|a|2)i2

|y1|=|y2|=|a|2+4|a|22=1

Hence, |y1|=|y2|=1

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometric Representation and Trigonometric Form
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon