1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
photoshop1234 [79]
3 years ago
10

Help appreciated on question in image! Thanks:)

Mathematics
2 answers:
Verdich [7]3 years ago
5 0

Answer:

x=-1,\:x=-7,\:x=i,\:x=-i

Step-by-step explanation:

Considering the equation

x^4+8x^3+8x^2+8x+7=0

Solving

x^4+8x^3+8x^2+8x+7

\mathrm{Factor\:}x^4+8x^3+8x^2+8x+7:\quad \left(x+1\right)\left(x+7\right)\left(x^2+1\right)

As

\mathrm{Use\:the\:rational\:root\:theorem}

a_0=7,\:\quad a_n=1

\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:7,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1

\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:7}{1}

-\frac{1}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+1

=\left(x+1\right)\frac{x^4+8x^3+8x^2+8x+7}{x+1}...[A]

Solving

\frac{x^4+8x^3+8x^2+8x+7}{x+1}

=x^3+7x^2+x+7

Putting \frac{x^4+8x^3+8x^2+8x+7}{x+1} =  x^3+7x^2+x+7 in equation [A]

So,

\left(x+1\right)\frac{x^4+8x^3+8x^2+8x+7}{x+1}...[A]

=\left(x+1\right)x^3+7x^2+x+7

As

x^3+7x^2+x+7=\left(x+7\right)\left(x^2+1\right)

So,

Equation [A] becomes

=\left(x+1\right)\left(x+7\right)\left(x^2+1\right)

So,  the polynomial equation becomes

\left(x+1\right)\left(x+7\right)\left(x^2+1\right)=0

\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)\mathrm{Solve\:}\:x+1=0:\quad x=-1

\mathrm{Solve\:}\:x+7=0:\quad x=-7

\mathrm{Solve\:}\:x^2+1=0:\quad x=i,\:x=-i

\mathrm{The\:solutions\:are}

x=-1,\:x=-7,\:x=i,\:x=-i

Keywords: polynomial equation

Learn polynomial equation from brainly.com/question/12240569

#learnwithBrainly

Katarina [22]3 years ago
3 0

Answer:

x^4+8x^3+8x^2+8x+7=0

Step-by-step explanation:

You might be interested in
To create an image, Figure D is going to be reflected across the y-axis, rotated 180° around the point indicated in the figure,
uranmaximum [27]
The image and pre-image are congruent
8 0
3 years ago
Select the expressions that are equivalent to 2(9r)
pashok25 [27]

Answer:

18r

Step-by-step explanation:

Multiply 9 by 2

5 0
3 years ago
To use energy efficiently, a certain washing machine should wash at least 2 kilograms of clothes. To avoid overloading the machi
agasfer [191]

Step-by-step explanation:

the answer is in the image above

7 0
3 years ago
The Venn Diagram below models probabilities of three events, A,B, and C.
Keith_Richards [23]

Answer: dependent

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Is 0.333 a natural number?
NeX [460]

Answer:

No, 0.333 is a rational number, not a natural number

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • A regular hexagon is shown below. Find the value of X
    15·1 answer
  • How many cubic feet of gas will a rectangular gas tank hold if it measures 15 ft x 4 ft x 6 ft?
    9·1 answer
  • Which of the following numbers are square roots of 64?<br> Check all that apply.
    10·2 answers
  • PLEASE HELP!!! WILL GIVE LOTS OF POINTS IF ANSWERED!!!
    8·1 answer
  • A right triangle has a 30o angle. the leg adjacent to the 30o angle measures 25 inches. what is the length of the other leg
    10·1 answer
  • at a recent party it cost $9.50 for drinks for 10 guests at the rate how much would it cost to have drinks for 80 guest
    8·2 answers
  • PLSSSSS HELP ME PLSSSSS I NEED TO EXPLAIN
    10·1 answer
  • Write a rule to describe the transformation on a graph
    12·1 answer
  • What are the odds of two threes being rolled by two 6-sided dice?<br><br> 1/?
    13·1 answer
  • Evaluate each of the following expressions by using special right triangles and the unit circle (give exact values),
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!