Find a bound on the real zeros of the polynomial function fx

Find a bound on the real zeros of the polynomial function f(x) = x^4 + 8x^3 -9x -5 Every real zero of f lies between

Solution

f(x) = x^4 +8x^3 -9x -5

Next we calculate two different \"bounds\" using those values:

f(x) = x^4 +8x^3 -9x -5

coefficients : 1 , 8 , -9 , -5

Drop the leading coefficient, and remove any minus signs: 8 ,9,5

Bound 1: the largest value is 9. Plus 1 = 10
• Bound 2: adding all values is: 8+9+5 = 22

smallest bound = 10

Real roots lie between -10 and 10