Question 1163519
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What assumption?  There are no assumptions in the problem as stated.<br>
It is a fact that the number of roots of a polynomial is equal to the degree of the polynomial.<br>
What is not true is your statement that the 4th degree polynomial has 5 roots -- it of course does not.<br>
Specifically, -1 is not a root.<br>
The roots are +/-.5 and -1+/-sqrt(2).<br>
If you ever think you are finding a n-th degree polynomial with more than n roots, check the work you did to determine the roots, because something in your calculations has to be wrong.<br>