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Mashutka [201]
2 years ago
12

How do I use the Descartes Rule of Signs to determine all possible number of positive and negative zeros?

Mathematics
1 answer:
larisa [96]2 years ago
8 0

Answer:

We conclude that:

  • 2  or 0 positive real roots
  • 2  or 0 negative real roots

Step-by-step explanation:

Descartes Rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is:

  • Either equal to the number of sign differences between consecutive nonzero coefficients,
  • Or is less than it by an even number.

Given the function

f\left(x\right)=x^4-2x^3-4x^2+2x+3

So, the coefficients are 1, −2, −4, 2, 3

As can be seen, there are 2 changes.

This means that there are 2 or 0 positive real roots.

To find the number of negative real roots, substitute x with -x in the given polynomial:

x^4-2x^3-4x^2+2x+3  becomes x^4+2x^3-4x^2-2x+3

The coefficients are 1, 2, −4, −2, 3

As can be seen, there are 2 changes.

This means that there are 2 or 0 negative real roots.

Therefore, we conclude that:

  • 2  or 0 positive real roots
  • 2  or 0 negative real roots

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After careful consideration i think I have an answer... 
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(by the way i'm going to be saying {the reflective side} every time i want to refer to the side with the two lines :P) - so bare with me. 

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So lets look over at the answers...

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For this answer choice, PN is on the non reflective side, while SQ is on the reflective side. Soooo... This answer choice is wrong. 

B.) NO = QR
NO  is part of the  unreflective side, while QR is part of the reflective side. 
Therefore this answer is wrong. They must be part of the same side. 

C.) ∠P = ∠S 
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There fore this answer is also wrong. 

D.) ∠O = ∠S 
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There fore this answer is correct . 

YOUR ANSWER IS. 
D.) ∠O = ∠S 

Good Luck! :)


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