Question

The polynomial of degree 4, p(x), has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0. What are the other roots of p(x)?

1) -1 and 2
2) -1 and -2
3) 1 and -2
4) 1 and 2

Answer 1

The polynomial p(x) of degree 4 has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0. Therefore, there is 1 more root for the polynomial p(x).

Step-by-step explanation:

The polynomial p(x) of degree 4 has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0. To find the other roots, we can use the fact that the total number of roots of a polynomial is equal to its degree. Therefore, the polynomial must have 4 roots in total. Since we already know that there are 2 roots at x=1 and 1 root at x=0, we subtract these known roots from the total number of roots to find the number of remaining roots: 4 - 2 - 1 = 1. So, there is 1 more root for the polynomial p(x).