14. Given that 16x⁴+ - 4x³– 4b²x² + 7bx + 18 is divisible by 2x + b,
(a) show that b³ - 7b² + 36 = 0,
(b) find the possible values of b.​

Answers

Answer 1

Answer:

(a) check the explanation

(b) the possible values of b is 6i or -29

Explanation:

Given function;

16x⁴ - 4x³– 4b²x² + 7bx + 18

(a)

factor of the given function = 2x + b

then, 2x + b = 0

x = -b/2

substitute the value of b into the given function;

16x⁴ - 4x³– 4b²x² + 7bx + 18

[tex]16(\frac{-b}{2} )^4 -4(\frac{-b}{2})^3-4b^2(\frac{-b}{2})^2 +7b(\frac{-b}{2})+18=0\\\\b^4+\frac{b^3}{2} -b^4-\frac{7b^2}{2} +18=0\\\\\frac{b^3}{2} -\frac{7b^2}{2} +18=0\\\\multiply\ through \ by \ "2"\\\\b^3-7b^2+36 =0 \ (shown)[/tex]

(b)

b³ - 7b² + 36 = 0

b²(b - 7) + 36 = 0

b²(b - 7) = -36

b² = -36                or b - 7 = -36

b = √(-36)             or  b = -36 + 7

b = √(-1) x √(36)   or  b = -29

b = 6i       or   -29              


Related Questions

What causes the wavelength of a particular beam of light change?

Answers

Answer:

Wave speed, frequency and wavelength in refraction

Explanation:

Although the wave slows down, its frequency remains the same, due to the fact that its wavelength is shorter. When waves travel from one medium to another the frequency never changes. As waves travel into the denser medium, they slow down and wavelength decreases.

Wave speed, wavelength in refraction and frequency causes the wavelength of a particular beam of light change.

What is wavelength of a light?

The wavelength of light is the separation between both the two crests or troughs of the light wave. It is recognized by the Greek letter lambda (). Therefore, the term "wavelength" refers to the distance between the crest or trough of one wave and the wave that follows it.

The number of waves that travel through a single location in a specific amount of time determines frequency, and the distance between two subsequent troughs or crests determines wavelength. As a result of the inverse connection between wavelength and frequency, frequency falls as wavelength increases.

The wave slows down, but because its wavelength is shorter, its frequency doesn't change. Waves' frequency does not alter as they go from one medium to another. Waves slow down and shorten in wavelength when they move through denser media.

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Which of the following is accurate about monsoons?
Check all that apply.
A. Heavy monsoons hurt the affected economies.
B. Indians prefer heavy monsoon seasons.
C. Monsoons create a perfect environment for rice farming.
D. Monsoons can cause devastating landslides and floods.

Answers

Answer:

D. Monsoons can cause devastating landslides and floods.

Explanation:

Monsoons require a large area of land and oceans, they occur where large bodies of water are limited to large land areas.

Monsoons are formed on the shores of certain oceans in both the southern and northern hemispheres. The most pronounced monsoons are formed over the Indian Ocean and the southern part of Asia. They come to it in the summer and start from the Himalayas during the winter.

Find the measure of the missing angles.
102°

Answers

They’re all congruent. They’re all 102
Answer
b=180-102=78
c=102

Rainforests are a feature of
the Columbia Basin.
the Olympic Mountains.
O the Puget Lowlands.
O the Willapa Hills.

Answers

Answer:

Rainforests are a feature of the Olympic Mountains.

Explanation:

The rainforests are something that is associated with the tropical regions around the Equator. This should not come as a surprise as the vast majority of them are found in this part of the world, but very often it is forgotten that there are other rainforests, outside of the tropics. These rainforests have all very similar characteristics to the tropical rainforests but they are located in the temperate regions in the mid-latitudes.

One such rainforest is found near the northwestern coast of the United States, in the state of Washington, on the Olympic Mountains. These mountains are located just above the coastline, and because they act as a barrier, the constant humidity that comes from the ocean is built up and there is rainfall throughout all of the year. Because there is rain all year round, there is lush vegetation, though it has to be noticed that the amount of plant species is relatively low compared to the tropical rainforests. The animal species tend to be in a higher number than in most of the other biomes in the temperate climates but again much smaller than in the tropical rainforests.

The Latin word vivere means to live. Based on this which of these is MOST LIKELY the meaning of the word rivere? A) to end life. B) to restore life. C) to withhold life. D) to carry out life

2

Answers

Answer:

It's to restore life

Explanation:

Everyone knows that the word revive means to restore a person's life/ restore something to it's former glory.

PLS HELP ASAP
The map that shows topography is called a _____ map.

political
climatic
physical
population

Answers

Answer: physical

Explanation:

Answer:

★ The answer is PHYSICAL

Explanation:

★ The map that shows topography is called a physical map.

Which statement describes a feature of a conic projection? (There is only one correct answer.)
A. Pilots use this projection type.
B. The equator usually serves as the central point.
C. Latitude lines connect at a central point.
D. Conic projections are the most distorted type.​

Answers

Answer:

the anser is A Pilots use this projection type.

Explanation:

hehe

The statement that can be considered as a feature of a conic projection as regards this question is :A. Pilots use this projection type.

Conic projection can be regarded as map projection whereby there is a projection of an area of the earth on to a cone, and in this case the vertex is been placed above one of the poles.

Conic projection are been utilized in mid-latitude zones having an (east–west) orientation.  It is been used by a pilot.

Therefore, option A is correct.

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