Question

How many real negative roots can this function possibly have? f(x) = 5x4 – 7x3 – x2 – 3x – 2

Answer 1

count the sign changes in f(-x)

Answer 2

f(-x) = 5(-x)^4 -7(-x)^3 -(-x)^2 -3(-x) -2

--> 5x^4 +7x^3 -x^2 +3x -2

--> pos, pos,neg,pos, neg

3 sign changes .... 1 or 3 possible neg roots