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
SVEN [57.7K]
3 years ago
10

Solve for x: x5 + x4 − 7x3 − 7x2 − 144x − 144 = 0

Mathematics
2 answers:
motikmotik3 years ago
6 0

x^5 + x^4 - 7x^3 - 7x^2 -144x - 144 = 0 \\x^4(x+1)-7x^2(x+1)-144(x+1)=0\\(x^4-7x^2-144)(x+1)=0\\\\x+1=0\Rightarrow x=-1\\\\x^4-7x^2-144=0\\x^4-16x^2+9x^2-144=0\\x^2(x^2-16)+9(x^2-16)=0\\(x^2+9)(x^2-16)=0\\(x^2+9)(x-4)(x+4)=0\\\\x^2+9=0\vee x-4=0 \vee x+4=0\\x=4 \vee x=-4\\\\x\in\{-4,-1,4\}

Zanzabum3 years ago
5 0

Answer:

{ -1, -3i,3i,4,-4}

Step-by-step explanation:

I'm going to try to get the Rational Root Theorem to work for us.

Since the coefficient of leading term is 1 we just need to look at the factors of the constant.

Possible rational zeros are going to be the factors of -144.

So here are some possible rational zeros: 1,2,3,4,6,8,9,12,16,18,24,36,48,72 and also the negative version of these numbers are numbers we must consider.

I'm going to see if -1 works.  

(-1)^5+(-1)^4-7(-1)^3-7(-1)^2-144(-1)-144

-1   +   1     +7      -7       +144  -144=0

So -1 is a zero so x+1 is a factor. I'm going to use synthetic division to see what multiplies to x+1 that will me the initial polynomial expression we had.

-1   |    1       1      -7        -7      -144    -144

     |           -1      0          7        0       144

     | ________ __________________

          1      0     -7         0       -144      0

So the (x+1)(x^4-7x^2-144)=0

The cool thing is that other factor is a sort of quadratic in disguise. That is it becomes a quadratic if you let u=x^2. So let's do that.

u^2-7u-144=0

(u+9)(u-16)=0

u=-9 or u=16

So x^2=-9 or x^2=16.

Square rooting both sides gives us:

x= \pm 3i \text{ or } x=\pm 4

So the solution set is { -1, -3i,3i,4,-4}

You might be interested in
YO!!!!WILL GIVE THE BRAIN!!!!!!!!
Tatiana [17]
The answer is b, since that's the only other function there that involves using absolute value
3 0
3 years ago
Read 2 more answers
Pls help asap!!!! tysm guys!!
Delvig [45]

Answer:

C. 256 in2

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Help please!!!!!!!!!
Alenkasestr [34]

Answer:

B. x^{2} - 4x - 5

Step-by-step explanation:

(p о n) (x) is the same thing as (p(n(x))

We know n(x) = x - 5, so let's input that into our expression

(p(x - 5))

Since we know p(x) = x^2 + 6x, let's replace the x with the new value x-5. Now our expression is:

p(x) = (x - 5)^2 + 6(x - 5)

Now all we have to do is simplify.

(x - 5)^2 is the same as:  (x - 5)(x - 5)

Using the foil method, it simplifies to:  x^2 - 10x + 25

6 (x - 5) = 6x - 30

Now our expression is:  x^2 - 10x + 25 + 6x - 30

Combine like terms:  x^2 - 4x - 5

The expression is: x^{2} - 4x - 5

5 0
3 years ago
Question is in picture.
Norma-Jean [14]

Answer:

<h2>B. 2x + y = 4</h2>

Step-by-step explanation:

Having the system of equations in its simplest form

\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right

If

a=d,\ b=e,\ c=f

then the system of equations has infinitely many solutions.

If

a=d,\ b=e,\ c\neq f

then the system of equations has no solution.

If

a\neq d\ or\ b\neq e

then the system of equations has one solution.

We have the equation

y=-2x+4

Convert to the standard form Ax + By = C<em>:</em>

<em />y=-2x+4<em>              add 2x to both sides</em>

y+2x=-2x+2x+4\\\\2x+y=4

3 0
3 years ago
When recording a transaction in a​ journal, the account listed first is always​ the:
GalinKa [24]

Answer:

da te

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • A picture is 6 inches longer than it is wide and has an area of 167
    10·1 answer
  • How can you find 5% of any number using mental math?
    7·2 answers
  • Based on this data what is reasonable estimate of the probability that it is sunny tomorrow
    8·2 answers
  • There are 9 boys to every 10 girls in a particular high school. there are 2622 students at the school. how many girls are there?
    13·1 answer
  • A 100-point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and the short response
    6·1 answer
  • 1 + hk + j use h=-5, j = -6, and k = 6<br> Help me
    15·1 answer
  • Someone please help me URGENT!!
    7·1 answer
  • What is 2 divided 1/5
    8·1 answer
  • Emma have 450000 dollars
    15·2 answers
  • Can someone help me please
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!