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3 years ago

Find the polynomial equation of least degree with roots -1, 3, and (+/-)3i

1 answer:

7 0

Each of these roots can be expressed as a binomial:

(x+1)=0, which solves to -1
(x-3)=0, which solves to 3
(x-3i)=0 which solves to 3i
(x+3i)=0, which solves to -3i
There are four roots, so our final equation will have x^4 as the least degree

Multiply them together. I'll multiply the i binomials first:
(x-3i)(x+3i) = x²+3ix-3ix-9i²
x²-9i²
x²+9 [since i²=-1]

Now I'll multiply the first two binomials together:
(x+1)(x-3) = x²-3x+x-3
x²-2x-3
Lastly, we'll multiply the two derived terms together:

(x²+9)(x²-2x-3) [from the binomial, I'll distribute the first term, then the second term, and I'll stack them so we can simply add like terms together]

x^4 -2x³-3x²
 +9x²-18x-27
x^4-2x³+6x²-18x-27

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2-3x=8 what does x equal?

juin [17]

If you would like to solve the equation 2 - 3 * x = 8 for x, you can calculate this using the following steps:

2 - 3 * x = 8
-3 * x = 8 - 2
-3 * x = 6 /(-3)
x = 6 / (-3)
x = -2

Result: x equals to -2.

7 0

3 years ago

Read 2 more answers

In a simple regression analysis (where y is a dependent and x an independent variable), if the y-intercept is positive, then it

Rom4ik [11]

Answer:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

$\bar x= \frac{\sum x_i}{n}$

$\bar y= \frac{\sum y_i}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x$

On this case the correct answer would be:

E. none of the above

Since the intercept has no association between the increase/decrease of the dependent variable respect to the independent variable

Step-by-step explanation:

Assuming the following options:

A. there is a positive correlation between X and Y

B. there is a negative correlation between X and Y

C. if X is increased, Y must also increase

D. if Y is increased, X must also increase

E. none of the above

If we want a model $y = mx +b$ where m represent the lope and b the intercept

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

$\bar x= \frac{\sum x_i}{n}$

$\bar y= \frac{\sum y_i}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x$

On this case the correct answer would be:

E. none of the above

Since the intercept has no association between the increase/decrease of the dependent variable respect to the independent variable

3 0

3 years ago

Transactions to a computer database are either new items or changes to previous items. the addition of an item can be completed

sashaice [31]

P(<100) = P((new or change) & <100) = P(new & <100) + P(change & <100)

... = P(<100 | new)*P(new) + P(<100 | change)*P(change)

... = 0.90*0.70 + 0.20*0.30

... = 0.63 + 0.06 = 0.69 . . . . probability of completing a transaction in < 100 ms

4 0

3 years ago

(01.06 LC) Which number is not in scientific notation?

Angelina_Jolie [31]

Answer:

$0.95*10^8$

Step-by-step explanation:

Hello!

Rules for scientific notation format:

Has to be multiplied to a power of 10
One factor has to be greater than 1 but less than 10

$\bold{0.95*10^8}$

There is a multiplication to a power of 10, but the other factor is less than 1.

This is NOT in Scientific Notation.

All the other options have a multiplication operation to a power of 10, and all the other factors are above 1 and less than 10.

3 0

2 years ago

Stefan buys a melon and divided into six servings he eat one third of the melon over the weekend how many slices of melon does S

kozerog [31]

2 slices of watermelon. He divides it into 6 slices and 1/3 of 6 is 2m

4 0

3 years ago