Problema Solution
Find the bounds on the real zeros of the following function. Please show all of your work.
f(x) = x4 + 5x3 – 2x2 + 4x – 1
Answer provided by our tutors
f(x) = x4 + 5x3 - 2x2 + 4x - 1
a3 = 5
a2 = -2
a1 = 4
a0 = -1
Max ( 1, |a0|+|a1|+|a2|+|a3|) = Max ( 1, 1+4+2+5) = Max(1,12) = 12
1+Max(|a0|,|a1|,|a2|,|a3|) = 1+ Max(1,4,2,5) = 1+5 = 6
The minimum value between 12 and 6 is 6
Then every zero of f(x) lies between -6 and 6