Question

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Answer 1

@mathmate can you check this?

Answer 2

@PRAETORIAN.10 can you help me?

Answer 3

dude you deffers got the wrong guy i suckkkkkkkkk at maths but i will give it a go anyways

Answer 4

f(x) = -3x^5 - 8x^4 +25x^3 - 8x^2 +x - 19
The coefficients change signs 4 times. It implies there is a MAXIMUM of 4 positive roots.

f(-x) = -3(-x)^5 - 8(-x)^4 +25(-x)^3 - 8(-x)^2 + (-x) - 19
f(-x) = 3x^5 - 8x^4 - 25x^3 - 8x^2 - x - 19
The coefficients change signs just once. It implies there is DEFINITELY ONE negative root.

For positive roots, you will have to decrease in steps of 2.

These are the possibilities:

Answer 5

Positive Negative Complex
Roots Roots Roots
4 1 0
2 1 2
0 1 4

Total in each row is 5 roots and since f(x) is a fifth degree polynomial there should be a total of 5 roots.

Answer 6

4 is the maximum possible positive roots. Descartes Rule of Signs does not guarantee there are 4 positive roots. You will have to decrease it in steps of 2 until it reaches 1 or 0. And you have to bump up the complex roots in twos because the total number of roots should be 5 for a fifth degree polynomial.

Answer 7

you are welcome.

Answer 8

yeah that other guy is correct as far as i can see