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kirill [66]
3 years ago
9

Find a degree 3 polynomial with real coefficients having zeros 4 and 4i and a lead coefficient of 1. Write P

Mathematics
1 answer:
melamori03 [73]3 years ago
4 0

Answer:

P(x)= x^3 - 4x^2 + 16x - 64

Step-by-step explanation:

First, let’s find all of the zeroes. If the question is asking for a degree 3 polynomial, than there has to be more than 2 zeroes. The complex conjugates theorem states that if a+bi is a zero, than a-bi has to be a zero as well. So if 4i is a zero, than -4i has to be a zero as well. By looking at the zeroes, you can write them as a linear factorization.

(x-4)(x+4i)(x-4i)

If you foil all of it, you will get x^3 - 4x^2 + 16x - 64.

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Look at the pentagonal numbers. Use finite differences to determine which function represents the pattern.
Ahat [919]

Answer:

f(x) = 1.5x - 0.5x

Step-by-step explanation:

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For  example,

The sequence

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* ,    *  *,     *   *   *,     *   *   *  *

_____________________________

The pentagonal numbers

The sequence:

1, 5, 12, 22, 35

As shown in the picture can be divided into three triangles

Triangle 2

x (x + 1) / 2

Triangle 1 and 3  (they are triangles one unit smaller than 2)

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Replacing n

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______________

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Ksivusya [100]
Thank you for posting your question here at brianly. I hope the answer will help you. Below is the solution:

or segment from (4,0) to (-4,0), y is always zero because straight segment. 
<span>in that case x*y=x*0=0 </span>
<span>and x+y=x+0=x </span>
<span>if you choose x=4-t where t goes from 0 to 8 you should get </span>
<span>r(t)=0i+(4-t)j </span>
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