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timama [110]
3 years ago
5

Write a polynomial function of least degree with the given zero. -1+ √ 2, √ 3

Mathematics
1 answer:
kirill115 [55]3 years ago
6 0

Answer:

f(x) = x^{4} + 2x³ - 4x² - 6x + 3

Step-by-step explanation:

Note that radical zeros occur in conjugate pairs, thus

- 1 + \sqrt{2} is a zero then - 1 - \sqrt{2} is also a zero

\sqrt{3} is a zero then - \sqrt{3} is also a zero

Thus the corresponding factors are

(x - (- 1 + \sqrt{2}) ), (x - (- 1 - \sqrt{2}) ), (x - \sqrt{3}), (x - (- \sqrt{3})), that is

(x + 1 - \sqrt{2}), (x + 1 + \sqrt{2}), (x - \sqrt{3}), (x + \sqrt{3})

The polynomial is then the product of the roots

f(x) = (x + 1 - \sqrt{2})(x + 1 + \sqrt{2})(x - \sqrt{3})(x + \sqrt{3})

     = ((x + 1)² - (\sqrt{2})²)((x² - (\sqrt{3})²)

     = (x² + 2x + 1 - 2)(x² - 3)

     = (x² + 2x - 1)(x² - 3) ← distribute

     = x^{4} - 3x² + 2x³ - 6x - x² + 3

     = x^{4} + 2x³ - 4x² - 6x + 3

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Step-by-step explanation:

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3 years ago
If an arena charges $7. 50 to park in satellite parking and $12. 00 to park in an arena lot, how much will be made from parking
Oksanka [162]

Parking 11,000 automobiles at the venue and 4,600 in satellites will bring in total $166,500.

<h3>Define multiplication.</h3>

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream.

Given,

If an arena charges $7. 50 to park in satellite parking and $12. 00 to park in an arena lot,

Multiplying:

$7.5 x 4,600 = satellite parking

$34,500 = satellite parking

The next step is to determine how much it will cost to park in the arena lot.

$11,000 ×12 = arena lot

$32,000 = arena lot

Let's now calculate the entire revenue from parking.

Total earnings equal $132,000 + $34,500.

Amount made in total is $166,500.

In conclusion Parking 11,000 automobiles at the venue and 4,600 in total satellites will bring in $166,500.

To learn more about multiplication, visit:

brainly.com/question/23354835

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3 0
11 months ago
What is the volume?
Alina [70]

Answer:

27 cubic unit

Step-by-step explanation:

as 27 is the product of three dimensions 3×3×3

5 0
2 years ago
An astronaut who weighs 85 kilograms on earth weighs 14.2 kilograms on the moon. How much would a person weigh on the moon if th
STatiana [176]

Answer:

Weight on the moon=x=15.87 kilograms

Step-by-step explanation:

This can be expressed as;

Weight on earth=Constant×Weight on moon

where;

Weight on moon=14.2 kilograms

Constant=k

Weight on Earth=85 kilograms

Replacing in the expression above;

85=14.2×k

k=(85/14.2)=5.986

If the person weighs 95 kilograms on Earth;

Weight on the earth=Constant×Weight on moon

where;

Weight on the moon=x

Constant=5.986

Weight on the earth=95 kilograms

Replacing;

95=5.986×x

x=95/5.986=15.87

Weight on the moon=x=15.87 kilograms

4 0
3 years ago
I need help finding the domain and range, I already know is not a function​
FromTheMoon [43]

Answer:

Domain: [-4, 4]

Range: [-3, 5]

Function? No

Step-by-step explanation:

Domain is all x-values that can be inputted in the graph that returns an output.

Range is all y-values that are outputted when <em>x</em> is inputted.

A function has to pass the Vertical Line Test.

6 0
3 years ago
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