6x^5-x^4+7x^3+x-1

Question

find the bound of the real zeros of the polynomial function

Answer 1

1. Coefficients: 6, - 1, 7, 1, - 1;
2. Dividing by 6: 1, -1/6, 7/6, 1/6, - 1/6
3. Drop leading coefficient and minuses: 1/6, 7/6, 1/6, 1/6

Bound 1: biggest value 7/6 plus 1 is 13/6

Bound 2: adding all values: 1/6 + 7/6 + 1/6 + 1/6 = 10/6 + 5/3

Smallest is 5/3

All real zeros between - 5/3 and 5/3