IF [(X-4)^5 -7(X-4)^4 +7(X-4)^3 -7(X-4)^2 +7(X-4)-6=0] FIND THE VALUE OF X??

Answer 1

Set y=x-4

If there is a rational solution, it must divide 6.

Negative solutions will not work because of the sign changes, i.e. for y<0 the polynomial is very large.

Try 6 by synthetic division...and you will get the root directly, i.e. y=6 and x=10.

Also if you simply graph the equation in y, you will see the root directly again.