nsider the following equation. 3x4 - 8x3 + 2 = 0, [2, 3] (a) Explain how we know that the given equation must have a root in the given interval. Let f(x) = 3x - 8x3 + 2. The polynomial f is continuous on [2, 3], f(2) = -14 v < 0, and f(3) = > 0, so by the Intermediate Value 29 Theorem, there is a number c in (2, 3) such that f(c) = . In other words, the equation 3x4 - 8x3 +2 = 0 has a root in [2, 3]. (b) Use Newton's method to approximate the root correct to six decimal places. 2.345067 leed Help?
nsider the following equation. 3x4 - 8x3 + 2 = 0, [2, 3] (a) Explain how we know that the given equation must have a root in the given interval. Let f(x) = 3x - 8x3 + 2. The polynomial f is continuous on [2, 3], f(2) = -14 v < 0, and f(3) = > 0, so by the Intermediate Value 29 Theorem, there is a number c in (2, 3) such that f(c) = . In other words, the equation 3x4 - 8x3 +2 = 0 has a root in [2, 3]. (b) Use Newton's method to approximate the root correct to six decimal places. 2.345067 leed Help?
Chapter5: Polynomial And Rational Functions
Section: Chapter Questions
Problem 17PT: Given the following information about a polynomial function, find the function. It has a double zero...
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![nsider the following equation.
3x4 - 8x3 + 2 = 0, [2, 3]
(a) Explain how we know that the given equation must have a root in the given interval.
Let f(x) = 3x - 8x3 + 2. The polynomial f is continuous on [2, 3],
f(2) = -14
v < 0, and f(3) =
> 0, so by the Intermediate Value
29
Theorem, there is a number c in (2, 3) such that f(c) =
. In other words,
the equation 3x4 - 8x3 +2 = 0 has a root in [2, 3].
(b) Use Newton's method to approximate the root correct to six decimal places.
2.345067
leed Help?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4544819-c947-4f88-88e4-9377318f4629%2F8a7454dc-c17a-46bb-9ad7-d2dc55a7cfb3%2Fjhu56ap_processed.png&w=3840&q=75)
Transcribed Image Text:nsider the following equation.
3x4 - 8x3 + 2 = 0, [2, 3]
(a) Explain how we know that the given equation must have a root in the given interval.
Let f(x) = 3x - 8x3 + 2. The polynomial f is continuous on [2, 3],
f(2) = -14
v < 0, and f(3) =
> 0, so by the Intermediate Value
29
Theorem, there is a number c in (2, 3) such that f(c) =
. In other words,
the equation 3x4 - 8x3 +2 = 0 has a root in [2, 3].
(b) Use Newton's method to approximate the root correct to six decimal places.
2.345067
leed Help?
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