the maximum number of zeros that the polynomial function may have. Then use Desc

Question

the maximum number of zeros that the polynomial function may have. Then use Descarte's Rule of Signs to determine how many positive and how many negative zeros the polynomial function may have. Do not attempt to find the zeros. f(x) = 6x^2 + 4x^6 + 5x^4 + 5x + 8. What is the maximum number of zeros that this polynomial function can have? ___ How many positive real zeros can the function have? __ (Use a comma to separate answers as needed.) How many negative real zeros can the function have? __ (Use a comma to separate answers as needed.)

Explanation / Answer

Degree = 7

So, max number of zeros = 7

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How many changes of sign in f(x)?
Absolutely none

So, 0 positive roots

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Now, we find f(-x),
which becomes
-6x&7 + 4x^6 + 5x^4 - 5x + 8

How many changes of sign?
3

So, negative roots can be either
3 or 1 in number

1 , 3

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