alyssamonett
Answered

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The polynomial function f(x) = -x^3 –x^2 + 4x +9 has one positive zero.
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Between what integers does this positive zero occur?

Sagot :

sqdancefan

Answer:

  between 2 and 3

Step-by-step explanation:

Positive rational roots will be one of 1, 3, or 9. The sum of coefficients is ...

  -1 -1 +4 +9 = 11

this tells us the root is greater than 1.

We can try f(3) to see if that is a root:

  f(3) = ((-3 -1)(3)+4)(3) +9 = (-12 +4)(3) +9 = -24 +9 = -15

This tells us the root is between 1 and 3. In order to narrow it further, we need to find f(2).

  f(2) = ((-2 -1)(2) +4)(2) +9 = (-6 +4)(2) +9 = 5

The sign of the function changes between f(2) > 0 and f(3) < 0, so the root is between the integer values 2 and 3.

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Additional comment

An iterative solution finds the irrational root to be near 2.34417122935.

View image sqdancefan
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