How to remove second term of the equation x4+8x3+x-5 =0 also prove that a field is necessarily an integral domain - Maths - Relations and Functions

Question

How to remove second term of the equation x4+8x3+x-5 =0 also prove
that a field is necessarily an integral domain but the converse is
not always true

Manasa Pallaki · Accepted Answer

Dear Student,

The given equation is  x4+8x3+x-5=0    
1Comparing it with ax4 + bx3 + cx2 + dx + e = 0we get a = 1; b = -8, c = 0; d = 1; e = -5 sum of  roots =-ba = -8since we have to remove the second term Diminishing the roots of 1 by -84=-2 we get
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_5842d313ce3ac%20png"
style="width: 556px; height: 319px;">
Transformed equation is y4-24y2+65y-55=0or when we express in x, we get, x4-24x2+65x-55=0

Regards

How to remove second term of the equation x4+8x3+x-5 =0 also prove that a field is necessarily an integral domain but the converse is not always true