Question

What are the possible number of positive, negative, and complex zeros of f(x) = –3x4 – 5x3 – x2 – 8x + 4 ?

Answer 1

we can use descartes rule of signes to solve this

Answer 2

agreed
count the change in signs for f(x)
-,-,-,-,+
There is 1 positive zero

count the change of signs for f(-x)
-,+,-,+,+
There are 3 changes so there could be 1 or 3 negative zeroes

Here are the possible zeroes, each row must total 4 since f(x) has degree of 4

Positive Negative Complex
1 1 2
1 3 0

Answer 3

Thank you so much!!!!! you're the best.