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lianna [129]
3 years ago
5

Find the zeros of the polynomial function f(x)=x^3-2x^2-8x

Mathematics
2 answers:
kotegsom [21]3 years ago
6 0
The roots are x=0,4,-2
KengaRu [80]3 years ago
5 0
First factor out that x
f(x)=x(x^2-2x-8)
what 2 numbers multiply to get -8 and add to get -2?
-4 and 2
f(x)=(x-0)(x-4)(x+2)
set to zero
x-0=0
x=0

x-4=0
x=4

x+2=0
x=-2

the zeroes are at x=-2,0 and 4
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Find the rule.
mezya [45]

The <em>first</em> series uses a <em>linear</em> function with - 1 as <em>first</em> element and 1 as <em>common</em> difference, then the rule corresponding to the series is y = |- 1 + x|.

The <em>second</em> series uses a <em>linear</em> function with - 3 as <em>second</em> element as 2 as <em>common</em> difference, then the rule corresponding to the series is y = |- 3 + 2 · x|.

<h3>What is the pattern and the function behind a given series?</h3>

In this problem we have two cases of <em>arithmetic</em> series, which are sets of elements generated by a condition in the form of <em>linear</em> function and inside <em>absolute</em> power. <em>Linear</em> <em>functions</em> used in these series are of the form:

y = a + r · x      (1)

Where:

  • a - Value of the first element of the series.
  • r - Common difference between two consecutive numbers of the series.
  • x - Index of the element of the series.

The <em>first</em> series uses a <em>linear</em> function with - 1 as <em>first</em> element and 1 as <em>common</em> difference, then the rule corresponding to the series is y = |- 1 + x|.

The <em>second</em> series uses a <em>linear</em> function with - 3 as <em>second</em> element as 2 as <em>common</em> difference, then the rule corresponding to the series is y = |- 3 + 2 · x|.

To learn more on series: brainly.com/question/15415793

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Explain how the graph of y = 2csc(x - pi/4) - 5 is related to the graph of the basic trigonometric function y = cscx.
Ymorist [56]

Answer: The distance between the min and max increased by a factor of 2, horizontally shifted to the right by \bold{\dfrac{\pi}{4}}, shifted down 5 units, and has a phase shift of \bold{\dfrac{\pi}{4}}

<u>Step-by-step explanation:</u>

The general form of a csc function is: y = A csc (Bx - C) + D  where

  • |A| is the amplitude (vertical stretch)
  • -A is a reflection over the x-axis
  • |B| is the horizontal stretch
  • -B is a reflection over the y-axis
  • C is a horizontal shift (left or right)
  • D is a vertical shift (up or down)

  • Period is \dfrac{2\pi}{B}
  • Phase Shift is \dfrac{C}{B}

In the given transformed graph y = 2 csc (x - \dfrac{\pi}{4}) - 5

  • A = 2   --> distance between the Min and max is 2(2) = 4
  • C = \dfrac{\pi}{4}  --> horizontally shifted to the right  \dfrac{\pi}{4} units
  • D = -5  --> shifted DOWN 5 units
  • Phase shift is \dfrac{\pi}{4}
3 0
3 years ago
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