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Helga [31]
3 years ago
6

Yo can someone help me out

Mathematics
1 answer:
Ivan3 years ago
5 0

Answer:

1=fee

Step-by-step explanation:

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Steve had 48 chocolates but decided to give 8 chocolates to each of his coworkers,
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Find a polynomial of degree 3 with real coefficients and zeros of -3,-1, and 4, for which f(-2)=-24
Zanzabum

We want to find a polynomial

<em>f(x)</em> = <em>a</em> <em>x</em>³ + <em>b</em> <em>x</em>² + <em>c</em> <em>x</em> + <em>d</em>

such that the roots of <em>f</em> are <em>x</em> = -3, <em>x</em> = -1, and <em>x</em> = 4, and <em>f(x)</em> takes on a value of -24 when <em>x</em> = -2.

The factor theorem for polynomials tells us that we can factorize <em>f(x)</em> as

<em>a</em> <em>x</em>³ + <em>b</em> <em>x</em>² + <em>c</em> <em>x</em> + <em>d</em> = <em>a</em> (<em>x</em> + 3) (<em>x</em> + 1) (<em>x</em> - 4)

Expand the right side:

(<em>x</em> + 3) (<em>x</em> + 1) (<em>x</em> - 4) = <em>x</em>³ - 13<em>x</em> - 12

So we have

<em>a</em> <em>x</em>³ + <em>b</em> <em>x</em>² + <em>c</em> <em>x</em> + <em>d</em> = <em>a x</em>³ - 13<em>a</em> <em>x</em> - 12<em>a</em>

<em />

In order for both sides to be equal, the coefficients of both polynomials on terms of the same degree must be equal. This means

<em>a</em> = <em>a</em> (of course)

<em>b</em> = 0 (there is no <em>x</em>² term on the right)

<em>c</em> = -13<em>a</em>

<em>d</em> = -12<em>a</em>

<em />

We also have that <em>f</em> (-2) = -24, which means

<em>f</em> (-2) = <em>a</em> (-2 + 3) (-2 + 1) (-2 - 4)

-24 = 6<em>a</em>

<em>a</em> = -4

which in turn tells us that <em>c</em> = 52 and <em>d</em> = 48.

So we found

<em>f(x)</em> = -4<em>x</em>³ + 52<em>x</em> + 48

4 0
3 years ago
Please help. I don’t understand how to do this
Rasek [7]

Greetings from Brasil...

Let's apply the given formula:

A = (1/2)·B·H

The base of this polygon (in this case, the triangle) is B

B = X² - 2X + 6

The height of this polygon is H and is H

H = X + 4

Applying these values (B and H) in the given formula.....

A = (1/2)·B·H

A = (1/2)·(X² - 2X + 6)·(X + 4)

A = (1/2)·(X³ + 2X² - 2X + 24)

A = (X³/2) + X² - X + 12

OR

A = (X³ + 2X² - 2X + 24)/2

4 0
3 years ago
Read 2 more answers
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