Question

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

Answer 1

@jiteshmeghwal9 can u help her? plz

Answer 2

wait i will be right back

Answer 3

Dude u must try to factor them first

Answer 4

mean the value of f(x)

Answer 5

@Katiebae use FACTOR THEOREM TO FACTORISE IT FIRST

Answer 6

By Descartes' Rule of Signs, determine the sign changes for both positive and negative cases.

Positive:

f(x) = 3x^4 - 5x³ - x² - 8x + 4

Two sign changes = two possible positive zeroes

Negative:

f(-x) = 3x^4 + 5x³ - x² + 8x + 4

Two sign changes = two possible negative zeroes or two possible imaginary zeroes.

Answer 7

OK.

Answer 8

Are there any complex? 4?

Answer 9

@Snapbacklive - Descartes' Rule of Signs is indeed the correct approach here.

However:
1. 2 sign changes in f(x) implies 2 or 0 positive roots
2. 2 sign changes in f(-x) implies 2 or 0 negative roots
3. This is a 4'th degree polynomial so 4 roots in total

so conclusion is:
a) 2 positive, 2 negative and 0 complex roots, or,
b) 0 positive, 0 negative and 4 complex roots.

Answer 10

Sorry - I made a mistake...

Answer 11

I haven't listed ALL possabilities

Answer 12

c) 2 positive, 0 negative and 2 complex
d) 0 positive, 2 negative and 2 complex

Answer 13

thanks to @ganeshie8 for REMINDING me to check my work! :)