Find the upper and lower bounds..

Question

Applying the first theorem on bounds for real zeros of polynomials, determine the smallest and largest integers that are upper and lower bounds, respectively, for the real solutions of the equation.

 

x⁴ − x³ − 2x² + 3x + 5 = 0

 

upper bound    lower bound    

 

Answer 1

upper bound is 4, the degree of the polynomial

lower bound is 0, as all 4 might be imaginary. They come in conjugate pairs, so they might be 0, 2 or 4 imaginary solutions.